NCERT Solutions for Class 6, 7, 8, 9, 10, 11 and 12
Knowing Our Numbers Class 6 Extra Questions Maths Chapter 1
June 11, 2019 by Bhagya
Extra Questions for Class 6 Maths Chapter 1 Knowing Our Numbers
Knowing Our Numbers Class 6 Extra Questions Very Short Answer Type
Question 1. Write the smallest three digit number whose value does not change on reversing its digits. Solution: The required number is 101.
Question 2. Write the greatest three digit number which does not change on reversing its digits. Solution: The required number is 999.
Question 3. What must be added to 203 to get a number whose digits are reversed of the given number? Solution: The number obtained by reversing the digits of 203 = 302. ∴ Difference = 302 – 203 = 99 Hence, the required number is 99.
Question 4. Write the following in Roman numerals: (a) 72 (b) 38 Solution: (a) 72 = LXXII (b) 38 – XXXVIII
Question 5. Write 438 in its expanded form. Solution: 438 = 4 x 100 + 3 x 10 + 8.
Question 6. Write the greatest five-digit number using the digits 4, 2 and 0. Solution: The greatest five-digit number using the digits 4, 2 and 0 is 44420.
Question 7. The capacity of a water tank is 300 litres. Express its capacity in millilitres. Solution: We know that 1 litre = 1000 mL ∴ 300 litres = 300 x 1000 mL = 3,00,000 mL Hence, the capacity of water tank = 3 lakh millilitres.
Question 8. What is the successor of greatest 6-digit number? Solution: Greatest 6-digit number = 999999 Successor of it = 999999 + 1 = 1000000 i. e., smallest 7-digit number. Hence, the required successor = 10,00,000.
Question 9. What is the place value of 7 in 1743? Solution: Let us write 1743 in its expanded form 1743 = 1000 + 700 + 40 +3 Place value of 7 = 700 Hence, the place value of 7 = 700.
Knowing Our Numbers Class 6 Extra Questions Short Answer Type
Question 11. Write the smallest and the greatest 5-digit numbers using the digits 0,2,4,6,8 (Repetition of digits is not allowed). Solution: Given digits are 0, 2, 4, 6, 8 5 – digit greatest number = 86420; 5 – digit smallest number = 20468.
Question 12. Write the following numbers in ascending order. How many of them are even numbers? 63,854, 63,584, 65,348, 68,543, 64,835 Solution: The given numbers are 63,854, 63,584, 65,348, 68,543 and 64,835. Ascending order is 63,584 ; 63,854 ; 64,835 ; 65,348 ; 68,543 Even numbers are 63,584, 63,854 and 65,348.
Question 13. Round the given numbers to the nearest tens. (a) 48 (b) 59 (c) 64 (d) 215 Solution: Given number Rounded off to tens (a) 48 → 50 (6) 59 → 60 (c) 64 → 60 (d) 215 → 220
Question 14. Estimate the following products: (а) 86 x 316 (b) 898 x 786 Solution: (a) 86 x 316 ∵ 86 → 90 [Rounding off to tens] and 316 → 320 [Rounding off to tens] So, the estimated product is 90 x 320 = 28800
(b) 898 x 786 ∵ 898 → 900 [Rounding off to hundreds] and 786 → 800 [Rounding off to hundreds] So, the estimated product is 900 x 800 = 720000.
Question 16. A student multiplied 3759 by 231 instead of multiplying by 213. How much was his product greater than the correct product? Solution: First Method: (3759 x 231)-(3759 x 213) = 868329 – 800667 = 67662 Second Method: 3759 x (231 – 213) = 3759 x 18 = 67662 Hence, the product difference is 67662.
Question 17. Estimate: 25,148 + 7394 + 9343 + 752 Solution: Estimated values are 25,148 → 25100 7394 → 7400 9343 → 9300 752 → 800 So, the estimated sum is 25100 + 7400 + 9300 + 800 = 42600 Hence, the estimated sum is 42600.
Question 18. Write all the even numbers between 90 and 100 in Roman Numerals. Solution: Even numbers between 90 and 100, we have 92, 94, 96, 98. ∴ 92 = XCII, 94 = XCIV, 96 = XCVI, 98 = XCVIII
Knowing Our Numbers Class 6 Extra Questions Long Answer Type
Question 20. Write Hindu-Arabic numerals for: (a) LXXXVI (b) LXXV (c) XCIX (d) XCI Solution: (a) LXXXVI = 50 + 30 + 6 = 86 (b) LXXV = 50 + 20 + 5 = 75 (c) XCIX = (100 – 10) + 9 = 99 (d) XCI = (100 – 10) + 1 = 91
Question 21. The distance between the school and Reena’s house is 1 km 480 m. Everyday she walks both ways. What distance does she cover in 6 days of a week? Solution: Distance covered when she walks one way = 1 km 480 m = 1480 m Therefore, the distance covered when she walk both ways in a day = 1480 x 2 m = 2960 m Total distance covered by Reena in 6 days = 2960 x 6 m = 17760 m or 17 km 760 m.
Question 24. Write each of the following numbers in figures: (a) Eighty-one million four hundred twelve thousand six hundred fifty. (b) Twenty million three hundred eighty thousand one hundred. (c) Ninety million nine. (d) Forty-nine million seven hundred eighty two thousand fifty eight. (e) Six millions three hundred fifty-two thousand nine hundred forty-six. (f) Seven crore twenty-three lakh eighty-six thousand, five hundred ninety-four. (g) Fifty crore forty lakh sixty thousand nine. (h) Nineteen crore, ninety lakh, fourteen thousand, six hundred eighty. Solution: In words In figure (а) Eighty-one millions four hundred twelve thousand, six hundred fifty. 81,412,650 (b) Twenty million three hundred eighty thousand one hundred 20,380,100 (c) Ninety million nine 90,000,009 (d) Forty-nine million seven hundred eighty-two thousand fifty-eight 49,782,058 (e) Six-millions three hundred fifty-two thousand nine hundred forty-six 6,352,946 (f) Seven crore, twenty-three lakh eighty-six thousand five hundred ninety-four 7,23,86,594 (g) Fifty crore forty lakh sixty thousand nine 50,40,60,009 (h) Nineteen crore ninety lakh fourteen thousand six hundred eighty. 19,90,14,680
Question 25. Write True/False for the following statements: (a) Roman symbol X cannot be repeated more than three times (b) VXXX = 25 …….. . (c) Estimate value of274 rounding off to nearest hundreds = 200 ……. (d) I and X can repeat at the most three times ……. (e) V, L and D are neither, repeated nor written to the left of greater value symbol …….. (f) There are six basic symbols in Roman Numeration system …….. Solution: (a) True (b) False (c) False (d) True (e) True (f) False.
Knowing Our Numbers Class 6 Extra Questions Higher Order Thinking Skills (HOTS)
Extra Questions for Class 6 Maths
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100 Best Case Study Questions for Your Next Customer Spotlight
Published: November 29, 2022
Case studies and testimonials are helpful to have in your arsenal. But to build an effective library, you need to ask the right case study questions. You also need to know how to write a case study .
Case studies are customers' stories that your sales team can use to share relevant content with prospects . Not only that, but case studies help you earn a prospect's trust, show them what life would be like as your customer, and validate that your product or service works for your clients.
Before you start building your library of case studies, check out our list of 100 case study questions to ask your clients. With this helpful guide, you'll have the know-how to build your narrative using the " Problem-Agitate-Solve " Method.
What makes a good case study questionnaire?
The ultimate list of case study questions, how to ask your customer for a case study, creating an effective case study.
Certain key elements make up a good case study questionnaire.
A questionnaire should never feel like an interrogation. Instead, aim to structure your case study questions like a conversation. Some of the essential things that your questionnaire should cover include:
- The problem faced by the client before choosing your organization.
- Why they chose your company.
- How your product solved the problem clients faced.
- The measurable results of the service provided.
- Data and metrics that prove the success of your service or product, if possible.
You can adapt these considerations based on how your customers use your product and the specific answers or quotes that you want to receive.
What makes a good case study question?
A good case study question delivers a powerful message to leads in the decision stage of your prospective buyer's journey.
Since your client has agreed to participate in a case study, they're likely enthusiastic about the service you provide. Thus, a good case study question hands the reins over to the client and opens a conversation.
Try asking open-ended questions to encourage your client to talk about the excellent service or product you provide.
Free Case Study Templates
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Categories for the Best Case Study Questions
- Case study questions about the customer's business
- Case study questions about the environment before the purchase
- Case study questions about the decision process
- Case study questions about the customer's business case
- Case study questions about the buying team and internal advocates
- Case study questions about customer success
- Case study questions about product feedback
- Case study questions about willingness to make referrals
- Case study question to prompt quote-worthy feedback
- Case study questions about the customers' future goals
Case Study Interview Questions About the Customer's Business
Knowing the customer's business is an excellent way of setting the tone for a case study.
Use these questions to get some background information about the company and its business goals. This information can be used to introduce the business at the beginning of the case study — plus, future prospects might resonate with their stories and become leads for you.
- Would you give me a quick overview of [company]? This is an opportunity for the client to describe their business in their own words. You'll get useful background information and it's an easy prompt to get the client talking.
- Can you describe your role? This will give you a better idea of the responsibilities they are subject to.
- How do your role and team fit into the company and its goals? Knowing how the team functions to achieve company goals will help you formulate how your solution involves all stakeholders.
- How long has your company been in business? Getting this information will help the reader gauge if pain points are specific to a startup or new company vs. a veteran company.
- How many employees do you have? Another great descriptor for readers to have. They can compare the featured company size with their own.
- Is your company revenue available? If so, what is it? This will give your readers background information on the featured company's gross sales.
- Who is your target customer? Knowing who the target audience is will help you provide a better overview of their market for your case study readers.
- How does our product help your team or company achieve its objectives? This is one of the most important questions because it is the basis of the case study. Get specifics on how your product provided a solution for your client. You want to be able to say "X company implemented our solution and achieved Y. "
- How are our companies aligned (mission, strategy, culture, etc.)? If any attributes of your company's mission or culture appealed to the client, call it out.
How many people are on your team? What are their roles? This will help describe key players within the organization and their impact on the implementation of your solution.
Case Study Interview Questions About the Environment Before the Purchase
A good case study is designed to build trust. Ask clients to describe the tools and processes they used before your product or service. These kinds of case study questions will highlight the business' need they had to fulfill and appeal to future clients.
- What was your team's process prior to using our product? This will give the reader a baseline to compare the results for your company's product.
- Were there any costs associated with the process prior to using our product? Was it more expensive? Was it worth the cost? How did the product affect the client's bottom line? This will be a useful metric to disclose if your company saved the client money or was more cost-efficient.
- What were the major pain points of your process prior to using our product? Describe these obstacles in detail. You want the reader to get as much information on the problem as possible as it sets up the reasoning for why your company's solution was implemented.
- Did our product replace a similar tool or is this the first time your team is using a product like this? Were they using a similar product? If so, having this information may give readers a reason to choose your brand over the competition.
- What other challenges were you and your team experiencing prior to using our product? The more details you can give readers regarding the client's struggles, the better. You want to paint a full picture of the challenges the client faced and how your company resolved them.
- Were there any concerns about how your customers would be impacted by using our product? Getting answers to this question will illustrate to readers the client's concerns about switching to your service. Your readers may have similar concerns and reading how your client worked through this process will be helpful.
- Why didn't you buy our product or a similar product earlier? Have the client describe any hesitations they had using your product. Their concerns may be relatable to potential leads.
- Were there any "dealbreakers" involved in your decision to become a customer? Describing how your company was able to provide a solution that worked within those parameters demonstrates how accommodating your brand is and how you put the customer first. It's also great to illustrate any unique challenges the client had. This better explains their situation to the reader.
- Did you have to make any changes you weren't anticipating once you became a customer? Readers of your case study can learn how switching to your product came with some unexpected changes (good or bad) and how they navigated them. If you helped your client with troubleshooting, ask them to explain that here.
How has your perception of the product changed since you've become a customer? Get the interviewee to describe how your product changed how they do business. This includes how your product accomplished what they previously thought was impossible.
Case Study Interview Questions About the Decision Process
Readers of the case study will be interested in which factors influenced the decision-making process for the client. If they can relate to that process, there's a bigger chance they'll buy your product.
The answers to these questions will help potential customers through their decision-making process.
- How did you hear about our product? If the client chose to work with you based on a recommendation or another positive case study, include that. It will demonstrate that you are a trusted brand with an established reputation for delivering results.
- How long had you been looking for a solution to this problem? This will add to the reader's understanding of how these particular challenges impacted the company before choosing your product.
- Were you comparing alternative solutions? Which ones? This will demonstrate to readers that the client explored other options before choosing your company.
- Would you describe a few of the reasons you decided to buy our product? Ask the interviewee to describe why they chose your product over the competition and any benefits your company offered that made you stand out.
- What were the criteria you used when deciding to buy our product? This will give readers more background insight into the factors that impacted their decision-making process.
- Were there any high-level initiatives or goals that prompted the decision to buy? For example, was this decision motivated by a company-wide vision? Prompt your clients to discuss what lead to the decision to work with you and how you're the obvious choice.
- What was the buying process like? Did you notice anything exceptional or any points of friction? This is an opportunity for the client to comment on how seamless and easy you make the buying process. Get them to describe what went well from start to finish.
- How would you have changed the buying process, if at all? This is an opportunity for you to fine-tune your process to accommodate future buyers.
- Who on your team was involved in the buying process? This will give readers more background on the key players involved from executives to project managers. With this information, readers can see who they may potentially need to involve in the decision-making process on their teams.
Case Study Interview Questions About the Customer's Business Case
Your case study questions should ask about your product or solution's impact on the customer's employees, teams, metrics, and goals. These questions allow the client to praise the value of your service and tell others exactly what benefits they derived from it.
When readers review your product or service's impact on the client, it enforces the belief that the case study is credible.
- How long have you been using our product? This will help readers gauge how long it took to see results and your overall satisfaction with the product or service.
- How many different people at your company use our product? This will help readers gauge how they can adapt the product to their teams if similar in size.
- Are there multiple departments or teams using our product? This will demonstrate how great of an impact your product has made across departments.
- How do you and your team currently use the product? What types of goals or tasks are you using the product to accomplish? Get specifics on how the product actively helps the client achieve their goals.
- If other teams or departments are using our product, do you know how they're using it? With this information, leads can picture how they can use your product across their teams and how it may improve their workflow and metrics.
- What was the most obvious advantage you felt our product offered during the sales process? The interviewee should explain the benefits they've gained from using your product or service. This is important for convincing other leads you are better than the competition.
- Were there any other advantages you discovered after using the product more regularly? Your interviewee may have experienced some additional benefits from using your product. Have them describe in detail what these advantages are and how they've helped the company improve.
- Are there any metrics or KPIs you track with our product? What are they? The more numbers and data the client can provide, the better.
- Were you tracking any metrics prior to using our product? What were they? This will allow readers to get a clear, before-and-after comparison of using your product.
- How has our product impacted your core metrics? This is an opportunity for your clients to drive home how your product assisted them in hitting their metrics and goals.
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Case Study Interview Questions About the Buying Team and Internal Advocates
See if there are any individuals at the customer's company who are advocates for your product.
- Are there any additional team members you consider to be advocates for our product? For example, does anyone stick out as a "power user" or product expert on your team? You may want to interview and include these power users in your case study as well. Consider asking them for tips on using your service or product.
- Is there anyone else on your team you think we should talk to? Again, the more people can share their experience using your product, the better.
- Are there any team members who you think might not be the biggest fans of our product or who might need more training? Providing extra support to those struggling with your product may improve their user experience and turn into an opportunity to not only learn about their obstacles but turn them into a product fan
- Would you share some details about how your team implemented our product? Get as much information as possible about the rollout. Hopefully, they'll gush about how seamless the process was.
- Who from your company was involved in implementing our product? This will give readers more insight into who needs to be involved for a successful rollout of their own.
- Were there any internal risks or additional costs involved with implementing our product? If so, how did you address them? This will give insight into the client's process and rollout and this case study question will likely provide tips on what potential leads should be on the lookout for.
- Is there a training process in place for your team's use of our product? If so, what does it look like? If your company provided support and training to the client, have them describe that experience.
- About how long does it take a new team member to get up to speed with our product? This will help leads determine how much time it will take to onboard an employee to your using your product. If a new user can quickly get started seamlessly, it bodes well for you.
- What was your main concern about rolling this product out to your company? Describing their challenges in detail will provide readers with useful insight.
- What have people been saying about our product since they started using it? Collect all the positive feedback you can to give your product more social proof.
Case Study Interview Questions About Customer Success
Has the customer found success with your product? Ask these questions to learn more.
- By using our product can you measure any reduced costs? If it has, you'll want to emphasize those savings in your case study.
- By using our product can you measure any improvements in productivity or time savings? Any metrics or specific stories your interviewee can provide will help demonstrate the value of your product.
- By using our product can you measure any increases in revenue or growth? Again, say it with numbers and data whenever possible.
- Are you likely to recommend our product to a friend or colleague? Recommendations from existing customers are some of the best marketing you can get.
- How has our product impacted your success? Your team's success? Getting the interviewee to describe how your product played an integral role in solving their challenges will show leads that they can also have success using your product.
- In the beginning, you had XYZ concerns; how do you feel about them now? Let them explain how working with your company eliminated those concerns.
- I noticed your team is currently doing XYZ with our product. Tell me more about how that helps your business. Illustrate to your readers how current customers are using your product to solve additional challenges. It will convey how versatile your product is.
- Have you thought about using our product for a new use case with your team or at your company? The more examples of use cases the client can provide, the better.
- How do you measure the value our product provides? Have the interviewee illustrate what metrics they use to gauge the product's success and how. Data is helpful, but you should go beyond the numbers. Maybe your product improved company morale and how teams work together.
- What will it take for you and your team to get the most value out of our product? This will help you dive deeper into how your client operates and how you can best assist them.
Case Study Interview Questions About Product Feedback
Ask the customer if they'd recommend your product to others. A strong recommendation will help potential clients be more open to purchasing your product.
- How do other companies in this industry solve the problems you had before you purchased our product? This will give you insight into how other companies may be functioning without your product and how you can assist them.
- Have you ever talked about our product to any of your clients or peers? What did you say? This can provide you with more leads and a chance to get a referral.
- Why would you recommend our product to a friend or client? Be sure they pinpoint which features they would highlight in a recommendation.
- Can you think of any use cases your customers might have for our product? Similar industries may have similar issues that need solutions. Your interviewee may be able to provide a use case you haven't come up with.
- What is your advice for other teams or companies who are tackling problems similar to those you had before you purchased our product? This is another opportunity for your client to talk up your product or service.
- Do you know someone in X industry who has similar problems to the ones you had prior to using our product? The client can make an introduction so you can interview them about their experience as well.
- I noticed you work with Company Y. Do you know if they are having any pain points with these processes? This will help you learn how your product has impacted your client's customers and gain insight into what can be improved.
- Does your company participate in any partner or referral programs? Having a strong referral program will help you increase leads and improve customer retention.
- Can I send you a referral kit as a thank-you for making a referral and give you the tools to refer someone to us? This is a great strategy to request a referral while rewarding your existing customers.
- Are you interested in working with us to produce additional marketing content? The more opportunities you can showcase happy customers, the better.
Case Study Interview Questions About Willingness to Make Referrals
- How likely are you to recommend our product to a friend or client? Ideally, they would definitely refer your product to someone they know.
- Can you think of any use cases your customers might have for our product? Again, your interviewee is a great source for more leads. Similar industries may have similar issues that need solutions. They may be able to provide a use case you haven't come up with.
- I noticed you work with Company Y; do you know if they are having any pain points with these processes? This will help you learn how your product has impacted your client's customers and gain insight into what can be improved.
Case Study Interview Questions to Prompt Quote-Worthy Feedback
Enhance your case study with quotable soundbites from the customer. By asking these questions, prospects have more insight into other clients and their success with your product — which helps build trust.
- How would you describe your process in one sentence prior to using our product? Ideally, this sentence would quickly and descriptively sum up the most prominent pain point or challenge with the previous process.
- What is your advice to others who might be considering our product? Readers can learn from your customer's experience.
- What would your team's workflow or process be like without our product? This will drive home the value your product provides and how essential it is to their business.
- Do you think the investment in our product was worthwhile? Why? Have your customer make the case for the value you provide.
- What would you say if we told you our product would soon be unavailable? What would this mean to you? Again, this illustrates how integral your product is to their business.
- How would you describe our product if you were explaining it to a friend? Your customers can often distill the value of your product to their friends better than you can.
- What do you love about your job? Your company? This gives the reader more background on your customer and their industry.
- What was the worst part of your process before you started using our product? Ideally, they'd reiterate how your product helped solve this challenge.
- What do you love about our product? Another great way to get the customer's opinion about what makes your product worth it.
- Why do you do business with us? Hopefully, your interviewee will share how wonderful your business relationship is.
Case Study Interview Questions About the Customers' Future Goals
Ask the customer about their goals, challenges, and plans for the future. This will provide insight into how a business can grow with your product.
- What are the biggest challenges on the horizon for your industry? Chances are potential leads within the same industry will have similar challenges.
- What are your goals for the next three months? Knowing their short-term goals will enable your company to get some quick wins for the client.
- How would you like to use our product to meet those challenges and goals? This will help potential leads understand that your product can help their business as they scale and grow.
- Is there anything we can do to help you and your team meet your goals? If you haven't covered it already, this will allow your interviewee to express how you can better assist them.
- Do you think you will buy more, less, or about the same amount of our product next year? This can help you gauge how your product is used and why.
- What are the growth plans for your company this year? Your team? This will help you gain insight into how your product can help them achieve future goals.
- How can we help you meet your long-term goals? Getting specifics on the needs of your clients will help you create a unique solution designed for their needs.
- What is the long-term impact of using our product? Get their feedback on how your product has created a lasting impact.
- Are there any initiatives that you personally would like to achieve that our product or team can help with? Again, you want to continue to provide products that help your customers excel.
- What will you need from us in the future? This will help you anticipate the customer's business needs.
- Is there anything we can do to improve our product or process for working together in the future? The more feedback you can get about what is and isn't working, the better.
Before you can start putting together your case study, you need to ask your customer's permission.
If you have a customer who's seen success with your product, reach out to them. Use this template to get started:
Thank you & quick request
Hi [customer name],
Thanks again for your business — working with you to [solve X, launch Y, take advantage of Z opportunity] has been extremely rewarding, and I'm looking forward to more collaboration in the future.
[Name of your company] is building a library of case studies to include on our site. We're looking for successful companies using [product] to solve interesting challenges, and your team immediately came to mind. Are you open to [customer company name] being featured?
It should be a lightweight process — [I, a product marketer] will ask you roughly [10, 15, 20] questions via email or phone about your experience and results. This case study will include a blurb about your company and a link to your homepage (which hopefully will make your SEO team happy!)
In any case, thank you again for the chance to work with you, and I hope you have a great week.
[Your name]
If one of your customers has recently passed along some praise (to you, their account manager, your boss; on an online forum; to another potential customer; etc.), then send them a version of this email:
Hey [customer name],
Thanks for the great feedback — I'm really glad to hear [product] is working well for you and that [customer company name] is getting the results you're looking for.
My team is actually in the process of building out our library of case studies, and I'd love to include your story. Happy to provide more details if you're potentially interested.
Either way, thank you again, and I look forward to getting more updates on your progress.
You can also find potential case study customers by usage or product data. For instance, maybe you see a company you sold to 10 months ago just bought eight more seats or upgraded to a new tier. Clearly, they're happy with the solution. Try this template:
I saw you just [invested in our X product; added Y more users; achieved Z product milestone]. Congratulations! I'd love to share your story using [product] with the world -- I think it's a great example of how our product + a dedicated team and a good strategy can achieve awesome results.
Are you open to being featured? If so, I'll send along more details.
Case Study Benefits
- Case studies are a form of customer advocacy.
- Case studies provide a joint-promotion opportunity.
- Case studies are easily sharable.
- Case studies build rapport with your customers.
- Case studies are less opinionated than customer reviews.
1. Case studies are a form of customer advocacy.
If you haven't noticed, customers aren't always quick to trust a brand's advertisements and sales strategies.
With every other brand claiming to be the best in the business, it's hard to sort exaggeration from reality.
This is the most important reason why case studies are effective. They are testimonials from your customers of your service. If someone is considering your business, a case study is a much more convincing piece of marketing or sales material than traditional advertising.
2. Case studies provide a joint-promotion opportunity.
Your business isn't the only one that benefits from a case study. Customers participating in case studies benefit, too.
Think about it. Case studies are free advertisements for your customers, not to mention the SEO factor, too. While they're not promoting their products or services, they're still getting the word out about their business. And, the case study highlights how successful their business is — showing interested leads that they're on the up and up.
3. Case studies are easily sharable.
No matter your role on the sales team, case studies are great to have on hand. You can easily share them with leads, prospects, and clients.
Whether you embed them on your website or save them as a PDF, you can simply send a link to share your case study with others. They can share that link with their peers and colleagues, and so on.
Case studies can also be useful during a sales pitch. In sales, timing is everything. If a customer is explaining a problem that was solved and discussed in your case study, you can quickly find the document and share it with them.
4. Case studies build rapport with your customers.
While case studies are very useful, they do require some back and forth with your customers to obtain the exact feedback you're looking for.
Even though time is involved, the good news is this builds rapport with your most loyal customers. You get to know them on a personal level, and they'll become more than just your most valuable clients.
And, the better the rapport you have with them, the more likely they'll be to recommend your business, products, or services to others.
5. Case studies are less opinionated than customer reviews.
Data is the difference between a case study and a review. Customer reviews are typically based on the customer's opinion of your brand. While they might write a glowing review, it's completely subjective and there's rarely empirical evidence supporting their claim.
Case studies, on the other hand, are more data-driven. While they'll still talk about how great your brand is, they support this claim with quantitative data that's relevant to the reader. It's hard to argue with data.
An effective case study must be genuine and credible. Your case study should explain why certain customers are the right fit for your business and how your company can help meet their specific needs. That way, someone in a similar situation can use your case study as a testimonial for why they should choose your business.
Use the case study questions above to create an ideal customer case study questionnaire. By asking your customers the right questions, you can obtain valuable feedback that can be shared with potential leads and convert them into loyal customers.
Editor’s Note: This article was originally published in June 2021 and has been updated for comprehensiveness.
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CBSE Class 6 Mathematics Knowing our Numbers Extra Questions
CBSE Class 6 Mathematics Knowing our Numbers Extra Questions. myCBSEguide has just released Chapter Wise Question Answers for class 6 Maths. There chapter wise Practice Questions with complete solutions are available for download in myCBSEguide website and mobile app. These Extra Questions with solution are prepared by our team of expert teachers who are teaching grade in CBSE schools for years. There are around 4-5 set of solved Mathematics Extra questions from each and every chapter. The students will not miss any concept in these Chapter wise question that are specially designed to tackle Exam. We have taken care of every single concept given in CBSE Class 6 Mathematics syllabus and questions are framed as per the latest marking scheme and blue print issued by CBSE for Class 6.
CBSE Class 6 Maths Extra Questions
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CBSE Class 6 Maths Chapter 1 Important Questions
Ch – 1 Knowing our Numbers
- None of these
- 10000000, 10000001, 10000002, 10000003, 10000004
- 10000001, 10000002, 10000003, 10000004, 10000005
- 10000004, 10000003, 10000002, 10000001, 10000000
- 7 8,92,10,92
- 7,89,21,092
- 1 2202, 7691
Match the following-
Fill in the blanks:
- 1 million = _____ hundred thousand.
- 1 crore = _____ ten lakh.
- 1 crore = _____ million.
- 1 million = _____ lakh.
State whether the following statements are true or false.
- 1 Thousand = 10 hundred.
- There are many Roman Numbers.
- You are using estimation to get rough idea.
- Standard unit of mass is centimetre.
- How many crores makes a billion?
- Find the greatest number from below number 763298 and 764298
- Place commas correctly and write the numerals : a) Seventy three lakh seventy five thousand three hundred seven. b) Nine crore five lakh forty one. c) Seven crore fifty two lakh twenty one thousand three hundred two. d) Fifty eight millions four hundred twenty three thousand two hundred two.
- On Sunday 6000 people visited a zoo. Among them 2615 were children then how many adult visited zoo?
- Kirti Bookstore sold books worth Rs.2,85,891 in the first week of June and books worth Rs.4,00,768 in the second week of the month. How much was the sale for the two weeks together? In which week was the sale greater and by how much?
- Find the greatest and the smallest number. 42375, 42367, 42329, 42338.
- Write and solve the expression: Thirteen multiplied by sum of four and eleven. Now reverse the result and add it to earlier result, what you obtain multiply it by 13.
- 10000000, 10000001, 10000002, 10000003, 10000004 Explanation: The smallest 8-digit number is 1,00,00,000 and the next four numbers are 1,00,00,001, 1,00,00,002, 1,00,00,003 and 1,00,00,004
- 24657 Explanation: The number has 4 in thousands place and 6 in hundreds place
- 1410 Explanation: 567 + 843 = 1410
- 12202, 124 Explanation: The number containing 5 digits is greater than the numbers containing digits 4 or 3 in short 5 digit number > 4 digit number > 3 digit number The number containing 3 digits is smaller than the numbers containing digits 4 or 5 in short 3 digit number < 4 digit number < 5 digit number
- {tex} \to {/tex} q
- {tex} \to {/tex} p
- {tex} \to {/tex} s
- {tex} \to {/tex} r
- 1 million = ten hundred thousand.
- 1 crore = ten ten lakh.
- 1 crore = ten million.
- 1 million = ten lakh.
- 1 billion= 100 crore
- 764298 is the greatest number
- a) 73,75,307 b) 9,05,00,041 c) 7,52,21,302 d) 58,423,202
- Total number of people visited the zoo = 6000 people Total number of children = 2615 children Then number of adults = 6000 – 2615 = 3385
- Sale of books in the first week = Rs.2,85,891. Sale of books in the second week = Rs.4,00,768 ∴ Sale for the two weeks together = Rs.2,85,891 + Rs.4,00,768 = Rs.6,86,659. The sale was greater in the second week by Rs. 4,00,768 – Rs.2,85,891 i.e., by Rs.1,14,877.
- The greatest number is 42375 The smallest number is 42329
- Expression 13 {tex} \times {/tex} (4 + 11) = 13 {tex} \times {/tex} 15= 195 On reversing the answer = 591 Adding reversing number to the result i.e. 591 + 195 = 786 Multiplying it by 13 i.e. 786 {tex} \times {/tex} 13= 10218.
Chapter Wise Extra Questions for Class 6 Mathematics
- Knowing our Numbers
- Whole Numbers
- Playing with Numbers
- Basic Geometrical Ideas
- Understanding Elementary Shapes
- Data handling
- Mensuration
- Ratio and Proportion
- Practical Geometry
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What Is a Case Study?
An in-depth study of one person, group, or event
Kendra Cherry, MS, is the author of the "Everything Psychology Book (2nd Edition)" and has written thousands of articles on diverse psychology topics. Kendra holds a Master of Science degree in education from Boise State University with a primary research interest in educational psychology and a Bachelor of Science in psychology from Idaho State University with additional coursework in substance use and case management.
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Benefits and Limitations
Types of case studies, how to write a case study.
A case study is an in-depth study of one person, group, or event. In a case study, nearly every aspect of the subject's life and history is analyzed to seek patterns and causes of behavior. Case studies can be used in various fields, including psychology, medicine, education, anthropology, political science, and social work.
The purpose of a case study is to learn as much as possible about an individual or group so that the information can be generalized to many others. Unfortunately, case studies tend to be highly subjective, and it is sometimes difficult to generalize results to a larger population.
While case studies focus on a single individual or group, they follow a format similar to other types of psychology writing. If you are writing a case study, it is important to follow the rules of APA format .
A case study can have both strengths and weaknesses. Researchers must consider these pros and cons before deciding if this type of study is appropriate for their needs.
One of the greatest advantages of a case study is that it allows researchers to investigate things that are often difficult to impossible to replicate in a lab. Some other benefits of a case study:
- Allows researchers to collect a great deal of information
- Give researchers the chance to collect information on rare or unusual cases
- Permits researchers to develop hypotheses that can be explored in experimental research
On the negative side, a case study:
- Cannot necessarily be generalized to the larger population
- Cannot demonstrate cause and effect
- May not be scientifically rigorous
- Can lead to bias
Researchers may choose to perform a case study if they are interested in exploring a unique or recently discovered phenomenon. The insights gained from such research can help the researchers develop additional ideas and study questions that might be explored in future studies.
However, it is important to remember that the insights gained from case studies cannot be used to determine cause and effect relationships between variables. However, case studies may be used to develop hypotheses that can then be addressed in experimental research.
Case Study Examples
There have been a number of notable case studies in the history of psychology. Much of Freud's work and theories were developed through the use of individual case studies. Some great examples of case studies in psychology include:
- Anna O : Anna O. was a pseudonym of a woman named Bertha Pappenheim, a patient of a physician named Josef Breuer. While she was never a patient of Freud's, Freud and Breuer discussed her case extensively. The woman was experiencing symptoms of a condition that was then known as hysteria and found that talking about her problems helped relieve her symptoms. Her case played an important part in the development of talk therapy as an approach to mental health treatment.
- Phineas Gage : Phineas Gage was a railroad employee who experienced a terrible accident in which an explosion sent a metal rod through his skull, damaging important portions of his brain. Gage recovered from his accident but was left with serious changes in both personality and behavior.
- Genie : Genie was a young girl subjected to horrific abuse and isolation. The case study of Genie allowed researchers to study whether language could be taught even after critical periods for language development had been missed. Her case also served as an example of how scientific research may interfere with treatment and lead to further abuse of vulnerable individuals.
Such cases demonstrate how case research can be used to study things that researchers could not replicate in experimental settings. In Genie's case, her horrific abuse had denied her the opportunity to learn language at critical points in her development.
This is clearly not something that researchers could ethically replicate, but conducting a case study on Genie allowed researchers the chance to study phenomena that are otherwise impossible to reproduce.
There are a few different types of case studies that psychologists and other researchers might utilize:
- Collective case studies : These involve studying a group of individuals. Researchers might study a group of people in a certain setting or look at an entire community. For example, psychologists might explore how access to resources in a community has affected the collective mental well-being of those living there.
- Descriptive case studies : These involve starting with a descriptive theory. The subjects are then observed, and the information gathered is compared to the pre-existing theory.
- Explanatory case studies : These are often used to do causal investigations. In other words, researchers are interested in looking at factors that may have caused certain things to occur.
- Exploratory case studies : These are sometimes used as a prelude to further, more in-depth research. This allows researchers to gather more information before developing their research questions and hypotheses .
- Instrumental case studies : These occur when the individual or group allows researchers to understand more than what is initially obvious to observers.
- Intrinsic case studies : This type of case study is when the researcher has a personal interest in the case. Jean Piaget's observations of his own children are good examples of how an intrinsic cast study can contribute to the development of a psychological theory.
The three main case study types often used are intrinsic, instrumental, and collective. Intrinsic case studies are useful for learning about unique cases. Instrumental case studies help look at an individual to learn more about a broader issue. A collective case study can be useful for looking at several cases simultaneously.
The type of case study that psychology researchers utilize depends on the unique characteristics of the situation as well as the case itself.
There are also different methods that can be used to conduct a case study, including prospective and retrospective case study methods.
Prospective case study methods are those in which an individual or group of people is observed in order to determine outcomes. For example, a group of individuals might be watched over an extended period of time to observe the progression of a particular disease.
Retrospective case study methods involve looking at historical information. For example, researchers might start with an outcome, such as a disease, and then work their way backward to look at information about the individual's life to determine risk factors that may have contributed to the onset of the illness.
Where to Find Data
There are a number of different sources and methods that researchers can use to gather information about an individual or group. Six major sources that have been identified by researchers are:
- Archival records : Census records, survey records, and name lists are examples of archival records.
- Direct observation : This strategy involves observing the subject, often in a natural setting . While an individual observer is sometimes used, it is more common to utilize a group of observers.
- Documents : Letters, newspaper articles, administrative records, etc., are the types of documents often used as sources.
- Interviews : Interviews are one of the most important methods for gathering information in case studies. An interview can involve structured survey questions or more open-ended questions.
- Participant observation : When the researcher serves as a participant in events and observes the actions and outcomes, it is called participant observation.
- Physical artifacts : Tools, objects, instruments, and other artifacts are often observed during a direct observation of the subject.
Section 1: A Case History
This section will have the following structure and content:
Background information : The first section of your paper will present your client's background. Include factors such as age, gender, work, health status, family mental health history, family and social relationships, drug and alcohol history, life difficulties, goals, and coping skills and weaknesses.
Description of the presenting problem : In the next section of your case study, you will describe the problem or symptoms that the client presented with.
Describe any physical, emotional, or sensory symptoms reported by the client. Thoughts, feelings, and perceptions related to the symptoms should also be noted. Any screening or diagnostic assessments that are used should also be described in detail and all scores reported.
Your diagnosis : Provide your diagnosis and give the appropriate Diagnostic and Statistical Manual code. Explain how you reached your diagnosis, how the client's symptoms fit the diagnostic criteria for the disorder(s), or any possible difficulties in reaching a diagnosis.
Section 2: Treatment Plan
This portion of the paper will address the chosen treatment for the condition. This might also include the theoretical basis for the chosen treatment or any other evidence that might exist to support why this approach was chosen.
- Cognitive behavioral approach : Explain how a cognitive behavioral therapist would approach treatment. Offer background information on cognitive behavioral therapy and describe the treatment sessions, client response, and outcome of this type of treatment. Make note of any difficulties or successes encountered by your client during treatment.
- Humanistic approach : Describe a humanistic approach that could be used to treat your client, such as client-centered therapy . Provide information on the type of treatment you chose, the client's reaction to the treatment, and the end result of this approach. Explain why the treatment was successful or unsuccessful.
- Psychoanalytic approach : Describe how a psychoanalytic therapist would view the client's problem. Provide some background on the psychoanalytic approach and cite relevant references. Explain how psychoanalytic therapy would be used to treat the client, how the client would respond to therapy, and the effectiveness of this treatment approach.
- Pharmacological approach : If treatment primarily involves the use of medications, explain which medications were used and why. Provide background on the effectiveness of these medications and how monotherapy may compare with an approach that combines medications with therapy or other treatments.
This section of a case study should also include information about the treatment goals, process, and outcomes.
When you are writing a case study, you should also include a section where you discuss the case study itself, including the strengths and limitiations of the study. You should note how the findings of your case study might support previous research.
In your discussion section, you should also describe some of the implications of your case study. What ideas or findings might require further exploration? How might researchers go about exploring some of these questions in additional studies?
Here are a few additional pointers to keep in mind when formatting your case study:
- Never refer to the subject of your case study as "the client." Instead, their name or a pseudonym.
- Read examples of case studies to gain an idea about the style and format.
- Remember to use APA format when citing references .
A Word From Verywell
Case studies can be a useful research tool, but they need to be used wisely. In many cases, they are best utilized in situations where conducting an experiment would be difficult or impossible. They are helpful for looking at unique situations and allow researchers to gather a great deal of information about a specific individual or group of people.
If you have been directed to write a case study for a psychology course, be sure to check with your instructor for any specific guidelines that you are required to follow. If you are writing your case study for professional publication, be sure to check with the publisher for their specific guidelines for submitting a case study.
Simply Psychology. Case Study Method .
Crowe S, Cresswell K, Robertson A, Huby G, Avery A, Sheikh A. The case study approach . BMC Med Res Methodol . 2011 Jun 27;11:100. doi:10.1186/1471-2288-11-100
Gagnon, Yves-Chantal. The Case Study as Research Method: A Practical Handbook . Canada, Chicago Review Press Incorporated DBA Independent Pub Group, 2010.
Yin, Robert K. Case Study Research and Applications: Design and Methods . United States, SAGE Publications, 2017.
By Kendra Cherry Kendra Cherry, MS, is the author of the "Everything Psychology Book (2nd Edition)" and has written thousands of articles on diverse psychology topics. Kendra holds a Master of Science degree in education from Boise State University with a primary research interest in educational psychology and a Bachelor of Science in psychology from Idaho State University with additional coursework in substance use and case management.
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6th Class Mathematics Knowing our Numbers Question Bank
Done knowing our numbers total questions - 55.
A) 7055 done clear
B) 7855 done clear
C) 7955 done clear
D) 8155 done clear
question_answer 2) In numbers from 1 to 100, how many times does the digit 0 appear?
A) 9 done clear
B) 10 done clear
C) 11 done clear
D) 12 done clear
question_answer 3) How many numbers are there containing 2 digits?
A) 90 done clear
B) 99 done clear
C) 100 done clear
D) 89 done clear
A) 4 done clear
B) 3 done clear
C) 2 done clear
D) 1 done clear
question_answer 5) Which of the following is the correct expansion of 27012?
A) 2000+700+0+10+2 done clear
B) 20000+700+0+10+2 done clear
C) 20000+1000+0+70+2 done clear
D) 20000+7000+0+10+2 done clear
question_answer 6) Which of the following is the greatest?
A) 7212 done clear
B) 7122 done clear
C) 7211 done clear
D) 7221 done clear
question_answer 7) Choose the correct ascending order of 6411, 6144, 6344, 6744.
A) 6144,6344,6411,6744 done clear
B) 6744,6411,6344,6144 done clear
C) 6344,6411,6144,6744 done clear
D) 6144,6411,6744,6344 done clear
question_answer 8) The smallest 4-digit number formed by using the digits 5,0,3,1 and 7 only once contains
A) 0 in thousands place. done clear
B) 5 in tens place. done clear
C) 3 in tens place. done clear
D) 7 in units place. done clear
question_answer 9) Write the greatest 4-digit number using different digits with 6 in the tens place.
A) 9876 done clear
B) 9867 done clear
C) 9687 done clear
D) 6987 done clear
question_answer 10) Round 3500 to the nearest thousand.
A) 3000 done clear
B) 3600 done clear
C) 4000 done clear
D) 4500 done clear
question_answer 11) Which of the following is the largest 8-digit number?
A) 888999 done clear
B) 99999999 done clear
C) 999999 done clear
D) 8999999 done clear
question_answer 12) Which is the smallest 9-digit number?
A) 900000000 done clear
B) 9 done clear
C) 100000000 done clear
D) 10000000 done clear
question_answer 13) What is the place value of 8 in the number 86, 93, 04, 600?
A) Eight crores done clear
B) Eighty crores done clear
C) Crores done clear
D) Eighty six crores done clear
question_answer 14) How many thousands is 1 lakh?
A) 1000 done clear
B) 100 done clear
C) 10 done clear
D) 10000 done clear
question_answer 15) Which is the place that comes on the immediate right of the hundreds place in the place value chart?
A) Thousands done clear
B) Tens done clear
C) Ones done clear
D) Ten thousands done clear
question_answer 16) What are the places in the millions period?
A) M, TM done clear
B) O, T, M done clear
C) M,TM, HM done clear
D) TTh, HTh, M done clear
question_answer 17) Under which period is ten lakhs?
A) Crores done clear
B) Lakhs done clear
C) Thousands done clear
D) Millions done clear
question_answer 18) How many millions are there in 10 crores?
A) 100 done clear
C) 1 done clear
D) 100 done clear
question_answer 19) Identify the symbol to be placed in the box \[\text{100002 }\,\square \text{ 1000002}\].
A) > done clear
B) < done clear
C) = done clear
D) : done clear
question_answer 20) How many crores make 1 billion?
A) 1 done clear
C) 100 done clear
D) 1000 done clear
question_answer 21) For which digit are the place value and face value always equal?
A) 0 done clear
B) 1 done clear
C) Any digit done clear
D) 10 done clear
question_answer 22) What is the predecessor of 80808080?
A) 80808099 done clear
B) 80808081 done clear
C) 80808079 done clear
D) 80808080 done clear
question_answer 23) What is the difference of the smallest 6-digit number and the greatest 4-digit number?
B) 90000 done clear
C) 90001 done clear
D) 900001 done clear
question_answer 24) Choose the correct statement.
A) 85868788 > 85878688 > 85888687 done clear
B) 85878688 > 85868788 > 85888687 done clear
C) 85868788 > 85888687 > 85878688 done clear
D) 85888687 > 85878688 > 85868788 done clear
question_answer 25) What is the face value of 3 in 31005660?
A) 3 crores done clear
B) 30 lakhs done clear
C) 3 done clear
D) 3 lakhs done clear
question_answer 26) What is the difference between the place values of the two 3s in 3116365?
A) 2999700 done clear
B) 3000700 done clear
C) 2990700 done clear
D) 3000005 done clear
question_answer 27) What is number of zeroes that come after 1 in 10 crores?
A) 6 done clear
B) 7 done clear
C) 8 done clear
D) 9 done clear
question_answer 28) Which of the following is the Roman numeral for the greatest three digit number?
A) IXIXIX done clear
B) CMIXIX done clear
C) CMXCIX done clear
D) CMIIC done clear
question_answer 29) What is the Hindu-Arabic numeral for MCDXVIII?
A) 1618 done clear
B) 1405 done clear
C) 1418 done clear
D) 1481 done clear
question_answer 30) What are the numerals that can be repeated in Roman System?
A) I, X and C done clear
B) I, V and X done clear
C) V, L and D done clear
D) D and L done clear
question_answer 31) What are the numerals that cannot be subtracted in Roman System?
A) V, L and D done clear
B) I, X and V done clear
C) C and X done clear
D) M and C done clear
question_answer 32) What is the Roman numeral for the difference of 500 and 200?
A) C done clear
B) CCC done clear
C) MMM done clear
D) D done clear
question_answer 33) Which of the following are the two numbers formed by subtracting I in Roman numerals?
A) 11 and 12 done clear
B) 4 and 10 done clear
C) 4 and 9 done clear
D) 5 and 6 done clear
question_answer 34) Anita's age is 48 years. How is her age represented in Roman System?
A) XXXXVIIII done clear
B) XLVII done clear
C) XLVIII done clear
D) XLV done clear
question_answer 35) Bobby's date of birth is 19th September. How is Bobby's date of birth represented in Roman System?
A) XXI done clear
B) XIXX done clear
C) IIX done clear
D) XIX done clear
question_answer 36) Raju is 22 years old and Ramu is 19 years old. How is the difference of their ages represented in Roman System?
A) III done clear
B) XXDI done clear
C) XXXLII done clear
D) XXXLL done clear
question_answer 37) What is the Roman numeral for 498?
A) CDCXVIII done clear
B) CDCXIV done clear
C) CDXCVIII done clear
D) CDXCVII done clear
question_answer 38) What is the Hindu-Arabic numeral for CCCXLVII?
A) 357 done clear
B) 347 done clear
C) 367 done clear
D) 387 done clear
question_answer 39) What is the number of matchsticks that can be used to write 39 in Roman System?
A) 8 done clear
B) 9 done clear
C) 3 done clear
D) 6 done clear
question_answer 40) What is the Roman numeral for the number obtained when 144 is divided by 16?
A) X done clear
B) VII done clear
C) VIII done clear
D) IX done clear
question_answer 41) How is the product obtained when 28 is multiplied by 2 represented in Roman System?
A) LIV done clear
B) LI I done clear
C) LVI done clear
D) LVII done clear
question_answer 42) How is the sum of CDI, V, C and X represented in Hindu-Arabic numeral?
A) 506 done clear
B) 401 done clear
C) 406 done clear
D) 516 done clear
question_answer 43) The number of boys in a class is 27 and the number of girls is 19. Write the total strength of the class in Roman numeral.
A) XLV done clear
B) XLIV done clear
C) XLVI done clear
D) XLVII done clear
question_answer 44) How many numerals are there in Roman numeration system?
A) 10 done clear
C) 8 done clear
D) 7 done clear
question_answer 45) What is the ascending order of XX, XXXVI, and V?
A) V XXXVI, XX done clear
B) XX, V, XXXVI done clear
C) V XX, XXXVI done clear
D) XXXVI, XX, V done clear
question_answer 46) What is the Roman numeral for 2143?
A) MMCXLIII done clear
B) MMCLIII done clear
C) MMCXLII done clear
D) VIIVIII done clear
question_answer 47) Which Roman numeral corresponds to the product obtained when 13 is multiplied by 7?
A) XXCI done clear
B) LXI done clear
C) XCI done clear
D) Cl done clear
question_answer 48) Which of the following is/are meaningless?
A) VX done clear
B) IXIV done clear
C) XIIV done clear
D) All the above done clear
question_answer 49) How many 8-digit numbers are there?
A) 99999999 done clear
B) 89999999 done clear
C) 90000000 done clear
D) 100000000 done clear
question_answer 50) What is the sum (21397 + 27807 + 42505) estimated to the nearest thousand?
A) 90000 done clear
B) 91000 done clear
C) 92000 done clear
D) 93000 done clear
question_answer 51) How is CDXLVI expressed in Hindu-Arabic numeral?
A) 456 done clear
B) 466 done clear
C) 436 done clear
D) 446 done clear
question_answer 52) How many times does the digit 3 appear in numbers from 1 to 100?
A) 18 done clear
B) 19 done clear
C) 20 done clear
D) 21 done clear
question_answer 53) How many numbers are there containing 3-digits?
A) 999 done clear
B) 899 done clear
C) 900 done clear
D) 800 done clear
question_answer 54) Write the smallest 5-digit number using three digits with 7 in the thousands place.
A) 77710 done clear
B) 17001 done clear
C) 07100 done clear
D) 17000 done clear
question_answer 55) What is the numeral for ninety million ninety thousand ninety?
A) 9, 090, 090 done clear
B) 90, 090, 090 done clear
C) 90, 90, 90 done clear
D) 90, 900, 900 done clear
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14 Best Case Study Questions to Ask Your Top Customers
If you want to show interested leads that you can put your money where your mouth is, case studies are a good way to go. They’re a valuable form of content that can even be used as lead magnets under the right conditions, and they have a singular purpose: To show how your clients achieved specific, significant results with your product or service.
Knowing how to write a great case study is an important part of success, but there’s a part of the process that comes before that: Knowing which questions to ask, which you’ll determine when you’re preparing for a case study interview.
The questions you ask can make the difference between a case study that feels like it’s been churned out by a low-quality AI machine compared to one that feels actionable, engaging, and high-stakes to your readers.
In this post, we’re going to go over the 14 best case study questions to ask, along with discussing some tips to improve the results you’ll get.
How to Structure Your Case Study Questions
Before we dive in, we want to talk about how to structure your questions in the interview.
In this post specifically, we’re going to look at individual questions you should ask around pointed topics, like about the client’s brand, solutions they’ve tried already, and their results.
It’s best to stick close to the progression outlined here because it will give you the basic information you need at every level of the case study interview . You can’t ask what solutions they’ve tried before when you don’t even understand their brands’ needs.
And keep in mind that when you’re asking users to provide specific information about a topic up front, they’ll often reference it later, strengthening the overall case study and sometimes encouraging them to share information they may not have thought to share otherwise.
That being said, let’s go ahead and start to dive in to the best case study questions you should ask.
Questions About Their Brand
The best case studies will have some information about the brand they’re featuring and not just about how the brand uses their product. Information about the brand size, industry, and unique selling propositions (USPs ) can all play a valuable part in building a strong case study.
These are a few important case study questions to consider asking about branding:
1. Can you tell us a little bit about your brand?
This is a great way to start the interview off strong. Ask the client to tell you about the brand, plain and simple. See what they have to say; they may share information about their product or service, how they fit into their industry, what differentiates them, and more.
Leaving this first question relatively vague and open-ended helps them feel more comfortable while giving you some good ideas for where to go.
If they’re stumped, ask them to provide a brief description of what their company does.
2. Can you tell me about your business’s structure, including industry, company size, or years in business?
While this may feel technical, it can be exceptionally valuable to readers of the case study to help them relate or get a good understanding of who is using your products.
3. An industry-relevant question
SaaS tools that help with ad management may ask clients about their total monthly ad spend, for example. An eco-friendly company may ask clients what their “green goals” are or their previous carbon emissions.
Think about what would benefit you to have in the case study, and ask it here if possible.
Questions About Their Challenge & Pain Points
We know that all great case studies will highlight the challenges that clients have before finding your product or service as their solution, exacerbated by key pain points.
It’s so important to get enough information that these challenges feel real and significant in the case study; if you neglect to explain why a challenge was an actual obstacle, it can come across as seeming trivial. That can make your solution seem trivial, too.
These are the best case study questions to ask for this stage of the interview.
4. What were the challenges you needed to solve before finding our product?
This is a specific, pointed question, which helps make it effective.
If I ask my content marketing clients this question, for example, they might say, “we didn’t know how to create content that ranked well” or “we needed help creating content at scale.”
You can dive deeper by asking pointed questions about their key problems, which brings us to the next question.
5. Why did this challenge have such a significant impact on your business?
This is the golden ticket right here, because it’s about pain points.
Say you’re selling marketing services, and the client’s challenge is that they wanted help with lead generation.
The pain points of “organic channels were too slow in driving customer acquisition, and our churn rates were eviscerating our client numbers” or “we tried to run ads ourselves but ended up losing hundreds of dollars to no avail.”
Wasted money. Bleeding clients. Too-slow organic channels. These are pain points that make the case study feel real, and that other customers will connect to.
6. What other solutions had you tried before and why didn’t they work?
While it’s best to skip out on trash-talking competitors in the case study, asking this question during the interview can give you valuable context and a lot to work with.
If, for example, I’m a weight loss coach, my clients may have tried the keto diet and Weight Watchers to no avail. Knowing that the keto diet made them feel queasy and that they found the point-tracking Weight Watchers to be too much work can be useful information for the study, even if you don’t ever name the alternatives.
These are pain points in their own right, and can be utilized like the following:
“The client had tried different solutions before but found that the diets either made them sick or were too much work to maintain.” It positions your solution to be the winning option.
Questions About How They Discovered You
While it may seem irrelevant, information about how customers discovered you and why they decided to work with you can actually become compelling parts of a case study— even if only mentioned in brief.
Here’s an example of how you can use this information in the case study:
“We found Breadcrumbs after our business partner mentioned it to us, and after reading about their easy-to-use interface and accessible lead scoring, we decided to give it a try.”
You’ve got social proof (business partner referred them) and a promo for a unique feature that made them convert.
Here are the case study questions you can ask to get this information:
7. How did you find out about our brand?
It’s a simple question, and it will likely be a simple answer. Nice and easy.
8. What made you decide to try our product over other solutions?
This essentially gets the customer to sell your product back to you, which is phenomenal. And someone reading the case study might think, “They’re right; I’ve also looked for a lead scoring tool with a great interface, I’d try that.”
Questions About How They Used The Product or Service
This will likely be one of the meatier parts of the case study interview because this is where some of the actionable information comes into play. How did your clients use your product or service, what steps did they take, and how can others use this to replicate the eventual results we’ll discover?
These are the case study questions to ask:
9. Which specific products and product features did your team use?
Say you’re selling invoicing software to small businesses. Not all clients will use every feature.
Graphic designers, for example, may take advantage of project estimates for upfront deposits more than a copywriter who only works for flat fees. That copywriter, however, might be more likely to use invoice templates for retainer clients or automated billing features.
Ask about the products and services the team used.
10. How did your team use our products and services to meet their needs?
You know what products or services were used, but now it’s time to ask how they were used.
Project estimates, for example, allowed graphic designers to send more professional-looking invoices to clients, who could pay upfront deposits through credit card, check, or bank deposit. This helped that designer weed out clients who had no intention of paying and gave them the funds they needed to secure the supplies to begin working.
And for the copywriter who used automated billing, it saved her an exceptional amount of time and ensured she got paid on time because she sent those invoices on time.
11. How was your experience?
Was the SaaS tool user-friendly? Did your clients take advantage of a free demo program or the option to have an account manager get their entire account up and running?
Ask about their specific transition process using the tool and what made the experience a more positive one.
Questions About Their Results
Last but not least… the results. Believe it or not, some case studies skip this part of the interview, but you definitely want to include hard, quantifiable data in as many case studies as possible.
12. What end results did you get after using our product?
Ask for the results your clients achieved. If they’re comfortable sharing the information, ask for KPIs.
How did using our social media marketing software increase message response rates?
How did our marketing service improve lead generation efforts, and customer acquisition costs?
How did our lead scoring software reduce the contact-to-close period for leads or increase the overall financial value of leads acquired?
Be as specific as the client will allow. The more definitive the data you can share, the better.
13. What impact did these results have on your business?
While this may seem self-explanatory, this is a great final question that again helps the impact of your product or service really stand out.
We saw customer satisfaction increase and sales go up by about 15% by improving message response rates on social media.
Or, by getting more leads at lower costs, our business was able to reinvest those accelerated profits into additional campaigns to scale exponentially at an unprecedented rate, and now we’re opening two new branches.
This can be a combination of data-focused or story-driven impacts. Either (or both!) works well.
14. Is there anything else we should know?
Anything else you want to share? This is a short but powerful question, and while some clients will say, “nope, that’s it,” you may be surprised what some other people share with you.
There may be something they’ve been excited to talk about that hasn’t come up in the questions yet, or something may pop into mind to elaborate on something you’d discussed earlier.
Give them the floor, and see what they have to say.
Final Thoughts
If you’re going to take the time needed to conduct and write up a case study (both your own time and the client’s), you want to get it right. Coming prepared with a list of strong case study questions can help you create content that will be highly effective at generating leads and converting customers for a long time to come.
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Knowing Your Numbers
If we look anywhere we will easily find the numbers around us. Your age, your class, your height each and every thing is related to the numbers. Isn’t this beautiful? Let’s learn more about the beauty of numbers and mathematics.
Comparing Numbers
Numbers can be compared whether they are large or small on the basis of their thousands, then hundreds, tens and even ones.
For example we can compare 2021 and 200 that 2021 is larger number because of its thousand values.
When we have to arrange objects according to some criteria, it can be done in two ways:
1) Ascending order : Ascending order means arrangement from the smallest to the greatest.
2) Descending order : Descending order means arrangement from the greatest to the smallest.
Example 1 : Arrange the numbers in descending order- 8754, 56, 9852, 124, 652.
Solution : In descending order we will start from largest number and end up in smallest hence the order will be
9852, 8754, 652, 124, 56.
On adding 1 to the largest two digit number we get the smallest three digit number. The same phenomenon is with all 3,4,5 digit numbers.
It means 99,999 is largest 5 digit number hence on adding 1 we get 1,00,000 smallest 6 digit number called lakh.
Revision of Place Values
In estimation we try to get close to the answer as much as possible by predicting all the possibilities. We make a rough idea about the case or condition.
Example 1 : Find the value of 63 x 987.
Solution : Since it is very difficult to find the product of such large numbers, therefore we are going to use estimation here.
We can say that 63 is close to 60 and 987 is close to 1000 and hence the product 63 x 987 will be close to 60 x 1000
And hence the value of 63 x 987 is close to 60,000.
Using Brackets
Sometimes we all come across some big mathematical expressions and to calculate the value we have to be very precise. Hence to solve such big mathematical expressions very easily we use brackets.
An important about brackets is to be remembered that they are solved first in any expression that is the expression written inside the bracket will be solved first.
Example 2 : Solve 17 x 109.
Solution : Solving such a big number’s multiplication is not very easy hence we will use brackets here
We can write 17 x 109 as
17 x 109 = (10+7) x 109
= 10 x 109 + 7 x 109
= 10 x (100+9) + 7 x (100 + 9)
= 10 x 100 + 10 x 9 + 7 x 100 + 7 x 9
= 1000 + 90 + 700 + 63
Roman Numerals
The numbers from 0 – 9 and also their magical combinations can also represented using certain alphabets and this representation is called Roman Numerals.
Example 3 : Write the roman numeral of 54.
Solution : Here we will use the brackets that is, we can write 54 as (50+4) = (L + V) = LV
Whole Numbers
- The number starting from 0 are called as whole numbers.
- The numbers staring from 1 are called as natural numbers.
- The successor of any number is next number that is +1 and predecessor is the previous number that is -1.
Whole numbers follows some properties which are:
- a) Addition and Multiplication are commutative for whole numbers. It means that if two whole numbers a and b are added and multiplied then,
a + b = b + a and a x b = b x a.
- b) ) Addition and Multiplication are associative for whole numbers. It means that if a, b and c are any three whole numbers then
a + (b + c) = (a + b) + c and a x ( b x c) = (a x b) x c.
Example 4 : Find the value of 4 x 25 x 564.
Solution : It is very difficult to find the product of such a large number hence we will use the property of associativity which means
4 x 25 x 564 = (4 x 25) x 564
= 100 x 564 = 56400.
Factor and Multiples
A factor of a number is an exact divisor of that number. For example factor of 12 is 1, 2, 3, 4, 6 and 12 itself are the factors of 12.
- 1 and the number itself are always the factors of the number.
- Every factor is always less than or equal to the number.
A number that may be divided by another a certain number of times without a remainder . For example, the multiple of 12 is 24, 48, 60 etc.
- Every multiple of a number is greater than or equal to that number .
- Every multiple of a number is greater than or equal to that number.
- Every number is a multiple of itself.
A number for which sum of all its factors is equal to twice the number is called a perfect number . The numbers 6 and 28 are perfect numbers.
Example 5: Find the factors and multiples of 45.
Solution : 45 = 1 x 45 45 = 3 x 15
Hence the factors are 1, 3, 5, 9, 15 , 45 .
Multiples will be 45, 90 , 135, 180 etc.
Prime and Composite Numbers
The numbers other than 1 whose only factors are 1 and the number itself are called Prime numbers.
Numbers having more than two factors are called composite numbers.
The numbers which are a multiple of 2 are called as even numbers. And the numbers which aren’t are called as odd numbers.
- 2 is the only even prime number and also the smallest prime number.
Divisibility Test
Divisibility by 2 : A number is divisible by 2 if it has any of the digits 0, 2, 4, 6 or 8 in its ones place.
Divisibility by 3: If the sum of the digits is a multiple of 3, then the number is divisible by 3.
Divisibility by 4: A number with 3 or more digits is divisible by 4 if the number formed by its last two digits (i.e. ones and tens) is divisible by 4.
Divisibility by 5: A number which has either 0 or 5 in its ones
place is divisible by 5.
Divisibility by 6: If a number is divisible by 2 and 3 both then it is divisible by 6 also.
Divisibility by 8: A number with 4 or more digits is divisible by 8, if the number formed by the last three digits is divisible by 8.
Divisibility by 9: If the sum of the digits of a number is divisible by 9, then the number itself is divisible by 9.
Divisibility by 10: if a number has 0 in the ones place then it is divisible by 10.
Divisibility by 11 : find the difference between the sum of the digits at odd places (from the right) and the sum of the digits at even places (from the right) of the number. If the difference is either 0 or divisible by 11, then the number is
divisible by 11.
Example 6 : Find whether the number 52749 is divisible by 9 or not ?
Solution: As we know that to check whether the number is divisible by 9 or not we must add the digits of the number.
Therefore on adding we get,
5 + 2 + 7 + 4 + 9 = 27
Since the number 27 is divisible by 9 hence the number 52749 is also divisible by 9.
Highest Common Factor (HCF) and Lowest Common Multiple (LCM)
The Highest Common Factor (HCF) of two or more given numbers is the highest (or greatest) of their common factors .
The Lowest Common Multiple (LCM) of two or more given numbers is the lowest (or smallest or least) of their common multiples.
Prime Factorization
When any number is written in the form of its factors, it is said to be factorized. And when the same number is factorized in terms of only prime numbers we call it prime factorization.
Example 7 : Find the prime factorization of 56 and 28 and hence find out the HCF.
Solution : The prime factorization of 56 = 2 x 2 x 2 x 7.
And the prime factorization of 28 = 2 x 2 x 7.
The HCF can be easily seen as 2 x 2 = 4.
Example 8 : Find the LCM of 20, 25 and 30.
Solution : The prime factorization of 20 = 2 x 2 x 5.
The prime factorization of 25 = 5 x 5.
The prime factorization of 30 = 2 x 3 x 5.
Here the prime number 2 appears for maximum 2 times, 3 for maximum 1 time, 5 for maximum 2 times.
Hence the LCM will be = (2 x 2) x 3 x (5 x 5) = 300.
Practice Questions
Q1) Arrange the numbers in increasing order 254, 87, 562 , 32564, 4581, 98778, 45, 12365, 456217.
Q2) Find the estimate product of 206 x 789.
Q3) Find the value of 27 x 104.
Q4) Write the following numbers in Roman numeral:
45,12, 32, 89 ,100.
Q5) Write the predecessor and successor of the following number: 1236, 789, 5474, 32658, 45789.
Q6) Check whether the number 12560 is divisible by 5 and 10 or not ?
Q7) Check whether the number 45847 is divisible by 6 and 9 or not ?
Q8) Find the HCF and LCM of the following numbers:
45 and 60, 30 and 150, 25 and 100.
- A factor of a number is an exact divisor of that number every number is a factor of itself. 1 is a factor of every number.
- Every number is a multiple of each of its factors every multiple of a given number is greater than or equal to that number every number is a multiple of itself.
- Commutativity, Associativity and Distributivity properties of whole numbers are useful in simplifying calculations and we use them without being aware of them.
- Zero is the identity for addition of whole numbers. The whole number 1 is the identity for multiplication of whole numbers.
- All natural numbers are whole numbers, but all whole numbers are not natural numbers.
- Every whole number has a successor. Every whole number except zero has a predecessor and every natural number has a successor. Every natural number except 1 has predecessor.
- We use the Hindu-Arabic system of numerals. Another system of writing numerals is Roman Numerals.
Quiz for Knowing Your Numbers
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Important Questions for Class 6 Maths Knowing our Numbers
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Unit: Knowing our numbers
Comparing numbers.
- Comparing multi-digit numbers (Opens a modal)
- Comparing multi-digit whole numbers word problems (Opens a modal)
- Compare multi-digit numbers Get 5 of 7 questions to level up!
- Compare multi-digit numbers word problems Get 3 of 4 questions to level up!
Large numbers
- Intro to lakhs and crores (Opens a modal)
- Reading and writing large numbers (Opens a modal)
- Intro to millions and billions (Opens a modal)
- Convert between lakhs, crores, millions, and billions Get 5 of 7 questions to level up!
- Word problems involving lakhs and crores Get 3 of 4 questions to level up!
Large numbers in practice
- Metric system: units of distance (Opens a modal)
- Metric system: units of volume (Opens a modal)
- Metric system: units of weight (Opens a modal)
- Multi-step unit conversion examples (metric) (Opens a modal)
- Convert to smaller units (mm, cm, m, & km) Get 5 of 7 questions to level up!
- Convert to smaller units (mL and L) Get 3 of 4 questions to level up!
- Convert to smaller units (g and kg) Get 3 of 4 questions to level up!
- Metric conversions word problems Get 3 of 4 questions to level up!
Estimating to nearest ten, hundred, or thousand
- Rounding to nearest 10 and 100 (Opens a modal)
- Rounding whole numbers to nearest thousand (Opens a modal)
- Round to nearest 10 or 100 on the number line Get 5 of 7 questions to level up!
- Round whole numbers Get 5 of 7 questions to level up!
Estimating sum, difference, or product
- Estimating adding and subtracting 3-digit numbers (Opens a modal)
- Multiplication estimation example (Opens a modal)
- Estimate to add multi-digit whole numbers Get 3 of 4 questions to level up!
- Estimate multi-digit multiplication problems Get 3 of 4 questions to level up!
Using brackets
- Evaluating expressions with & without parentheses (Opens a modal)
- Constructing numerical expressions (Opens a modal)
- Evaluate expressions with parentheses Get 5 of 7 questions to level up!
- Translate expressions with parentheses Get 3 of 4 questions to level up!
Roman numerals
- Intro to Roman numerals (Opens a modal)
- Reading and writing Roman numerals (Opens a modal)
- Roman numerals worked example (Opens a modal)
- Read Roman numerals Get 3 of 4 questions to level up!
- Convert to Roman numerals Get 3 of 4 questions to level up!
Sample Case Study Questions and Answers
Get the Best Sample Case Study Questions and Answers
A case study is an excellent study for the college as well as university students. It is a detailed study regarding the problem in any particular company. Students need to find the best solution to this problem with the help of their managerial, leadership and analytical skills.
The case study questions are usually asked by many business schools while offering the MBA (Master of business administration) as well as other managerial degree courses. You need to prepare very well for these case study questions in order to get admissions in the business school of your choice. They judge the most potential students to study in their institution.
The case study question is also asked during your managerial course, where the faculties ask questions in the case study report presented to you as an assignment. You also need to prepare us for getting the top grades in these case study questions. A reputed Case Study Sample Free online service provider will always be an excellent help for you in qualifying and getting good grades in your case study question sessions. In this blog, we will discuss the best ways to answer the case study questions on various topics and companies.
How to Answer the Case Study Question?
The case study questions can be of various types. It depends on the managerial specialization you are having. If you are a student of marketing management, the fooling can be a few case study questions for you.
- What is the marketing strategy of the motor manufacturing company X in Australia?
- How can company Y do the best market segmentation in the USA?
- Give a proper SWOT analysis of company X
- Define BCG matrix with a practical example
- Define PERTEL analysis with an appropriate example
- How can you fix the prices of product y?
- How to do the best market survey of company X?
- How can you know what your target customers need by as useful market survey?
- How to set the questionnaires for the best market survey?
- How to do online marketing of services and products?
- What are the best modes of marketing?
- How to maximize the chances of profits and minimize the chances of future losses of company X?
- What will be the best market planning for company Y in Canberra?
- What can be the most effective marketing strategies for any software or IT (Information Technology) company to establish the business at any foreign nation/
- What is your idea on local as well as international marketing strategies?
You need to give the best answers to all these questions with relevant and practical examples from the current industry. You can also take the assistance on an excellent online Case Study Assignment Help service provider who will give you free samples on various case study questions answers. You can get a good idea on how to answer multiple case study questions and provide the best solutions for the top grades.
Some Common Questions on Financial Management Case Study Are As Follows:
- What is retrograde pricing?
- How to fix the annual budget for company X?
- What are financial models to be used to maximize the future profit of company X?
- What is financial leveraging?
- How to increase cash flow?
- How to set the company dividend?
- What are the rules of success for company Y in the financial field?
- Why did X private bank fail in the global market?
- How to fix costing and pricing of the product?
- Why company X declined due to national economic slowdown?
- How to adapt the best financial strategies to ensure long-term profits for any organization?
- How to save company expenses?
- How to get the best financial auditing results?
The scenario of any particular company or organization will be given to answer each of these questions. You can take the help of a case study analysis assignment writing online service in this regard. Apart o this you can also add a few real-life practical examples in the financial fields in the present local as well as global industry. A financial case study answer sample can help you in this regard. From these samples, you can get a clear idea on how to write the case study answers following a proper method and format. This will help you in getting better grades.
Some Common Questions on Human Resource Management (HRM)
- How can company X form the best plan for employee performance appraisal?
- How can company Y control the staff attrition rate?
- What are the best ways to reduce the HR cost of any organization?
- How can a well-planned workforce system help the performance of company A?
- How to do a proper HR auditing?
- What were the main reasons of Enron failure?
- How companies like Xerox and Cadbury reached the top?
- What is whistle blown and how to control it?
- How to manage the staff salary issues?
Here also you will be given the questions based on the HR issues of a particular organization. A reliable online Essays Writing Service provider can guide you the best in providing the best answers to all these questions. They will also provide the best practical and industrial examples and reference for you.
A Few Questions on Operations Management
- What are the Delphi and six sigma techniques of operands management?
- How to apply the best operating management models for the welfare of the company?
- How too the best forecasting by operations management statistical models?
- How to help in the final production of company X?
Here, the case study answers are also to be given in the same way and with a lot of examples d illustrations. In your case study answers, you always need to provide the best solute regard any issue in the any of the menial departments of the given company. You also need to explain the valid reasons to your assessors why you selected that particular solution. Thus, you need to undergo studies and right preparing before appearing or your case study interview sessions. These types of interviews can be both written and oral. You need to prepare differently for these 2 types of sessions. A case study helps service providers cab guide you ideally in this respect.
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MCQ Questions for Class 6 Maths Chapter 1 Knowing Our Numbers with Answers
Students can access the NCERT MCQ Questions for Class 6 Maths Chapter 1 Knowing Our Numbers Pdf free download aids in your exam preparation and you can get a good hold of the chapter. Use MCQ Questions for Class 6 Maths with Answers during preparation and score maximum marks in the exam. Students can download the Knowing Our Numbers Class 6 MCQs Questions with Answers from here and test their problem-solving skills. Clear all the fundamentals and prepare thoroughly for the exam taking help from Class 6 Maths Chapter 1 Knowing Our Numbers Objective Questions.
Knowing Our Numbers Class 6 MCQs Questions with Answers
Students are advised to solve Knowing Our Numbers Multiple Choice Questions of Class 6 Maths to know different concepts. Practicing the MCQ Questions on Knowing Our Numbers Class 6 with answers will boost your confidence thereby helping you score well in the exam.
Explore numerous MCQ Questions of Knowing Our Numbers Class 6 with answers provided with detailed solutions by looking below.
Question 1. The smallest 8 digit number is called (a) Ten lakh (b) One lakh (c) Ten crore (d) One crore
Answer: (d) One crore
Question 2. Which of the following is not a symbol to write Roman numerals? (a) D (b) V (c) M (d) N
Answer: (d) N
Question 3. If we add 1 more to the greatest 5-digit number we get (a) Smallest 5-digit number (b) Smallest 4-digit number (c) Smallest 3-digit number (d) Smallest 6-digit number
Answer: (d) Smallest 6-digit number
Question 4. The smallest 4-digit number using any one digit twice from the numbers 2, 8, 9 is : (a) 2889 (b) 2289 (c) 2298 (d) 2898
Answer: (b) 2289
Question 5. The smallest 4-digit number having three different digits is: (a) 1000 (b) 1203 (c) 1320 (d) 1002
Answer: (d) 1002
Question 6. Which of the following options is equal to MMMCCLXXV − MCCCXXIV? (a) MLMCI (b) MMCLI (c) MCMLI (d) MCMIL
Answer: (c) MCMLI
We want to round this to the thousandths place .
Question 7. Which pair has same digits at hundreds place? (a) 4232, 4341 (b) 5432, 6922 (c) 6524, 7823 (d) 2334, 2340
Answer: (d) 2334, 2340
Question 8. Which of the following options is true? (a) XCVIII > MCVIII (b) DCVIII < MCVIII (c) DCVIII = MCVIII (d) XCVIII < LXXXVII
Answer: (b) DCVIII < MCVIII
Question 9. The greatest 4-digit number using any one digit twice from the numbers 7, 1, 2 is : (a) 7221 (b) 7721 (c) 7122 (d) 7112
Answer: (b) 7721
Question 10. The difference between face value and place value of 5 in 210517 is: (a) 4995 (b) 5005 (c) 495 (d) 395
Answer: (c) 495
Question 11. Make the greatest four digit number by using any one digit twice by 3, 8, 7? (a) 8378 (b) 8873 (c) 3387 (d) 7783
Answer: (b) 8873
Question 12. Write the greatest 4-digit number using different digits with 6 in the tens place. (a) 9876 (b) 9867 (c) 9687 (d) 6987
Answer: (b) 9867
Question 13. Which of the following is the Roman numeral for the number 2765? (a) MMDCCXLV (b) MMDCXLXV (c) MMDCCLXV (d) MMCDCLXV
Answer: (c) MMDCCLXV
Question 14. The smallest 4-digit number using the digits 2, 1, 3, 7 without repetition is : (a) 1237 (b) 2137 (c) 2371 (d) 3217
Answer: (a) 1237
Question 15. In the Indian place value system we write ten crores for: (a) One million (b) Ten millions (c) Hundred millions (d) None of these
Answer: (c) Hundred millions
Question 16. Face value of 5 in 2150 is: (a) 5 (b) 50 (c) 500 (d) 5000
Answer: (b) 50
Question 17. Predecessor of 1997 is: (a) 1998 (b) 1996 (c) 2000 (d) 1995
Answer: (b) 1996
Question 18. The greatest 4-digit number using the digits 4, 7, 3, 2 without repetition is : (a) 2374 (b) 3247 (c) 4723 (d) 7432
Answer: (d) 7432
Question 19. Correct ascending order of 847, 9754, 8320, 571 is (a) 9754, 847, 8320, 571 (b) 571, 847, 8320, 9754 (c) 571, 8320, 847, 9754 (d) 9754, 8320, 847, 571
Answer: (b) 571, 847, 8320, 9754
Question 20. The least number that is divisible by all the numbers from 1 to 10 (both inclusive) is (a) 10 (b) 100 (c) 504 (d) 2520
Answer: (d) 2520
Question 21. The successor of 999 is: (a) 1000 (b) 1001 (c) 998 (d) 1002
Answer: (a) 1000
Question 22. Which number is the greatest? (a) 8142 (b) 4821 (c) 8412 (d) 8241
Answer: (c) 8412
Question 23. Write the numeral for the number Nine crore five lakh forty-one. (a) 90500410 (b) 90500041 (c) 95000041 (d) None of these
Answer: (b) 90500041
Question 24. What is the place value of 8 in the number 86,93,04,600? (a) Eight crores (b) Eighty crores (c) Crores (d) Eighty six crores
Answer: (b) Eighty crores
Question 25. The smallest 5-digit number formed by using the digits 5,0,3,1 and 2 only once (a) 10325 (b) 01235 (c) 10235 (d) 20135
Answer: (c) 10235
Question 26. Which of the following is the greatest? (a) 7212 (b) 7122 (c) 7211 (d) 7221
Answer: (d) 7221
Question 27. Make the greatest four digit number by using any one digit twice by 0, 4, 9? (a) 9404 (b) 9440 (c) 9940 (d) 9400
Answer: (c) 9940
Question 28. The smallest 3-digit number using the digits 3, 5, 2 without repetition is (a) 532 (b) 253 (c) 235 (d) 352
Answer: (c) 235
Question 29. In the international system of numeration we write one million for: (a) Ten lakhs (b) One lakh (c) Hundred thousands (d) Ten thousands
Answer: (a) Ten lakhs
Question 30. Make the greatest and the smallest four digit number using any four-digit number with digit 5 always at thousand place. (a) 5999, 5000 (b) 5789, 5120 (c) 5986, 5012 (d) 5987, 5012
Answer: (a) 5999, 5000
Question 31. One crore is similar to (a) 10 hundreds (b) 100 thousands (c) 1000 lakhs (d) 100 lakhs
Answer: (d) 100 lakhs
Question 32. Which number is the smallest? (a) 70621 (b) 20671 (c) 60265 (d) 60315
Answer: (b) 20671
Question 33. Which of the following options is written in the ascending order? (a) XCVII > XCCIV > DCCLXVIII > MDCLXII (b) MDCLXII < DCCLXVIII < XCCIV < XCVII (c) MDCLXII > DCCLXVIII > XCCIV > XCVII (d) XCVII < XCCIV < DCCLXVIII < MDCLXII
Answer: (d) XCVII < XCCIV < DCCLXVIII < MDCLXII
Question 34. XX is equivalent to: (a) 10 (b) 20 (c) 30 (d) 40
Answer: (b) 20
Question 35. Place value of 6 in 2617 is: (a) 6 (b) 60 (c) 600 (d) 6000
Answer: (a) 6
Question 36. he greatest 3-digit number using the digits 2,1, 5 without repetition is: (a) 215 (b) 125 (c) 521 (d) 152
Answer: (c) 521
Question 37. Expand the number 345600. (a) Three lakh six hundred (b) Forty-five thousand six hundred (c) Three lakh forty-five thousand (d) Three lakh forty-five thousand six hundred
Answer: (d) Three lakh forty-five thousand six hundred
Question 38. If we add 1 more to the greatest 2-digit number we get (a) Smallest 4-digit number (b) Smallest 6-digit number (c) Smallest 3-digit number (d) Smallest 5-digit number
Answer: (c) Smallest 3-digit number
Question 39. If we add 1 more to the greatest 3-digit number we get (a) Smallest 4-digit number (b) Smallest 7-digit number (c) Smallest 5-digit number (d) Smallest 6-digit number
Answer: (a) Smallest 4-digit number
Question 40. One crore is equal to: (a) 1 million (b) 10 millions (c) 100 millions (d) 1000 millions
Answer: (b) 10 millions
Question 41. Which number is the smallest? (a) 2571 (b) 1278 (c) 7218 (d) 1226
Answer: (d) 1226
Question 42. Which of the following options is correct according to the rules of writing Roman numerals? (a) DDXC (b) MDCLXXI (c) XDVII (d) CLLVV
Answer: (b) MDCLXXI
Question 43. Which of the following is shown as a repetition of symbols to write Roman numerals? (a) Multiplication (b) Subtraction (c) Addition (d) Division
Answer: (c) Addition
Question 44. 3,00,000 + 4,000 + 800 + 7 is equal to: (a) 344807 (b) 304807 (c) 300807 (d) 480407
Answer: (b) 304807
Question 45. Which number is the greatest? (a) 2361 (b) 2136 (c) 1236 (d) 6123
Answer: (d) 6123
Question 46. When 1 is subtracted from smallest 5-digit number, what is the result? (a) Greatest 2-digit number (b) Greatest 3-digit number (c) Greatest 4-digit number (d) Smallest 2-digit number
Answer: (c) Greatest 4-digit number
Fill in the blanks:
1. The greatest number in 8142, 8214, 8412 is …………………..
Answer: 8412
2. The smallest 4-digit number is …………………….
Answer: 1000
3. 4231 taken to nearest thousand is …………………
Answer: 4000
4. The smallest number in 20051, 15020, 50120, 51200 is ………………..
Answer: 20051
5. The greatest 5-digit number is ……………………
Answer: 99999
6. Successor of 125 is ……………….
Answer: 126
7. Place value of 6 in 26349 is ………………..
Answer: 6000
8. Seventy thousand seven is written in figures as …………………
Answer: 70007
9. 241 taken to nearest hundred is ………………..
Answer: 200
10. Predecessor of 3980 is: ………………………..
Answer: 3979
Match the numerals:
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- What Is a Case Study? | Definition, Examples & Methods
What Is a Case Study? | Definition, Examples & Methods
Published on May 8, 2019 by Shona McCombes . Revised on January 30, 2023.
A case study is a detailed study of a specific subject, such as a person, group, place, event, organization, or phenomenon. Case studies are commonly used in social, educational, clinical, and business research.
A case study research design usually involves qualitative methods , but quantitative methods are sometimes also used. Case studies are good for describing , comparing, evaluating and understanding different aspects of a research problem .
Table of contents
When to do a case study, step 1: select a case, step 2: build a theoretical framework, step 3: collect your data, step 4: describe and analyze the case.
A case study is an appropriate research design when you want to gain concrete, contextual, in-depth knowledge about a specific real-world subject. It allows you to explore the key characteristics, meanings, and implications of the case.
Case studies are often a good choice in a thesis or dissertation . They keep your project focused and manageable when you don’t have the time or resources to do large-scale research.
You might use just one complex case study where you explore a single subject in depth, or conduct multiple case studies to compare and illuminate different aspects of your research problem.
Once you have developed your problem statement and research questions , you should be ready to choose the specific case that you want to focus on. A good case study should have the potential to:
- Provide new or unexpected insights into the subject
- Challenge or complicate existing assumptions and theories
- Propose practical courses of action to resolve a problem
- Open up new directions for future research
Unlike quantitative or experimental research , a strong case study does not require a random or representative sample. In fact, case studies often deliberately focus on unusual, neglected, or outlying cases which may shed new light on the research problem.
However, you can also choose a more common or representative case to exemplify a particular category, experience or phenomenon.
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While case studies focus more on concrete details than general theories, they should usually have some connection with theory in the field. This way the case study is not just an isolated description, but is integrated into existing knowledge about the topic. It might aim to:
- Exemplify a theory by showing how it explains the case under investigation
- Expand on a theory by uncovering new concepts and ideas that need to be incorporated
- Challenge a theory by exploring an outlier case that doesn’t fit with established assumptions
To ensure that your analysis of the case has a solid academic grounding, you should conduct a literature review of sources related to the topic and develop a theoretical framework . This means identifying key concepts and theories to guide your analysis and interpretation.
There are many different research methods you can use to collect data on your subject. Case studies tend to focus on qualitative data using methods such as interviews , observations , and analysis of primary and secondary sources (e.g., newspaper articles, photographs, official records). Sometimes a case study will also collect quantitative data.
The aim is to gain as thorough an understanding as possible of the case and its context.
In writing up the case study, you need to bring together all the relevant aspects to give as complete a picture as possible of the subject.
How you report your findings depends on the type of research you are doing. Some case studies are structured like a standard scientific paper or thesis , with separate sections or chapters for the methods , results and discussion .
Others are written in a more narrative style, aiming to explore the case from various angles and analyze its meanings and implications (for example, by using textual analysis or discourse analysis ).
In all cases, though, make sure to give contextual details about the case, connect it back to the literature and theory, and discuss how it fits into wider patterns or debates.
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- Knowing our Numbers
Knowing our numbers- An overview
Knowing our Numbers is the first chapter in NCERT for the 6th class. It is very important to go through this chapter thoroughly as it would create a foundation for students for the further chapters in the book. The topics that are discussed in this chapter are listed below-
Introduction
Comparing numbers, large numbers in practice, using brackets, roman numerals.
The first section is the introduction which introduces the importance of numbers that help us to count or arrange the objects and are used in many different contexts. These are arithmetic values that help us to convey the magnitude of all the objects that are present around us.
In order to understand mathematical concepts such as greater than or equal to, the comparison of numbers is important. The subtopics of comparing numbers are:
How many numbers can you make?
In this part, students will learn how they can make numbers from given digits. Numbers will be formed in such a way that no digit is repeated in a single number and there cannot be two exact numbers. Students will also learn about the different orders of numbers which are ascending (smallest to greatest) and descending (greatest to smallest).
Shifting digits
In this part, students will learn how a small shift in the digits of the numbers can make a difference in the value of the number.
Introducing 10,000
In this part, students learn about the greatest 3-digit number which is 999, and what happens when we add a 1 to 999.
Revisiting place value
In this part, students will learn about the expansion of 2-digit, 3-digit, and 4-digit numbers and the place value for each digit.
Introducing 1,00,000
In this part, students will learn about the greatest 5-digit number which is 99999, and what happens when 1 is added to 99999.
Larger Numbers
In this section, students will learn about the greatest and smallest 6-digit, 7-digit, and 8-digit numbers which include numbers like 10 lakh and one crore.
An aid in reading and writing large numbers
This section will explain to the students how to read and write large numbers by identifying the digits in one place, tens place, hundreds place, and so on.
Use of commas
This chapter will also help the students to learn the use and importance of commas in the number system.
Students will learn about large numbers and how they can be written in shorter forms by using units such as centimeters and meters, grams and kilograms, meters and kilometers, etc.
This section will help the students to learn about the approximate or near values of certain numbers. Let us have a look at the subsections.
Estimating the nearest tens by rounding off
In this section, students will learn how to round off numbers to the nearest tens. Suppose 13 is a number that lies between 10 and 20, but since it is closer to 10, therefore it would be rounded off to the nearest tens which are 10.
Estimating the nearest hundreds by rounding off
Here students will learn how to round off numbers to the nearest hundreds, for example, 310 lies between 300 and 400 but are closer to 300, therefore it will be rounded off to 300.
Estimating the nearest thousands by rounding off
Just like nearest tens and hundreds, students will also learn about how to round off numbers to the nearest thousand. For example, 8600 is a number that lies between 8000 and 9000 but since it is closer to 9000, it would be rounded off to the nearest thousand which is 9000.
Estimating outcomes of number situations
Students will learn about the situations where we need to answer quickly for how to add numbers quickly by keeping the digits of the numbers being added in the same place and rounding them off to the nearest values.
To estimate sum or difference
It is not always necessary that you need to round off, therefore in this section students will learn why and when we need to round off.
To estimate products
Here the students will learn about the general rule which states that estimating while multiplying can be done by rounding off each factor to its greatest place and then multiplying those factors.
Students will learn about the use of brackets and how they are used in order to avoid confusion while doing mathematical calculations. In expanding brackets the students will learn the systematic procedure for the removal of brackets.
Students will study one of the earliest systems which are roman numerals and are still used in many places
FAQs on Knowing our Numbers
1. What is estimation in mathematics? How to round off numbers?
Estimation in mathematics is making an assumption or rounding off a particular number for better understanding and quick calculation. For instance, 25,158 people have attended a recent football match. However, for better reference, this number is rounded-off to its nearest round number, i.e. either 25,000 or 25,500.
On the other hand, referring 25,128 as 26,000 is not a correct estimation. Additionally, to round off numbers using this method, you can take help of the estimation and use the nearest estimated number. You can use this estimation method to perform mathematical operations as well. Moreover, this method helps in quick calculation and representing an exact figure that is often difficult to calculate.
2. Which is the lowest five-digit number?
10, 000 is the smallest five-digit number. Moreover, it appears by adding 1 with the highest four-digit number, i.e. 9,999. The pattern followed for this calculation is, 9+1=10=10X1; 99+1=100=100X1; 999+1=1000=1000X1; 9,999+1=10,000=10,000X1.
Furthermore, you can use this method to calculate an even larger number with six, seven-digits. This process further explains that, highest single-digit number + 1 = smallest two-digit number; greatest two-digit number + 1 = smallest three-digit number; highest three-digit number + 1 = smallest four-digit number, and so on.
3. What is the International System of Numeration?
Similar to the Indian system of numeration, there is an International system of numeration. However, unlike the Indian system, here commas mark thousands and millions. One million is equal to a thousand thousands.
Moreover, in this system, commas come after every three-digit from the right. Here the first one marks thousand and the next one is for millions. For instance, 45,520,598 is read as forty-five million five hundred twenty thousand five hundred and ninety-eight according to the international system. On the other hand, in the Indian system, it will be read as four crores fifty-five lakhs twenty thousand five hundred and ninety-eight.
Additionally, in the international system, billion is used to denote any number larger than millions. Thus, 1 billion = 1000 million.
4. What is the purpose of a comma?
Commas play a pivotal role in writing, learning and remembering large numbers. The Indian System of Numeration uses ones, tens, thousands, lakhs and then crores. Commas help in marking these. Moreover, in the Indian system commas are used in indicating thousands, lakhs, and then crores.
Furthermore, the initial comma comes after hundreds place, i.e. three digits from the right. After that, the second comma comes after two digits, which marks lakh. Finally, the third comma comes after another two digits, i.e. seven digits from the right. Thus, it marks crore.
5. What are Some of the Importance of Estimation of Numbers?
Estimation is one of the most important skills that one possesses and it is not possible for the students to determine if the answer is correct or not if they lack these skills. Estimation of numbers is important as it helps to possibly determine the correct and reasonable answers. Estimations can make a calculation quicker, easier, and realistic if done properly.
6. What is the Reason behind studying Roman Numerals?
Roman numerals are a part of the numerical system that was studied in ancient Rome. The numerals include combinations of letters from Latin alphabets which are used to represent different values. Studying Roman numerals may help the students in understanding the ancient roman culture and think about numbers in different ways.
7. What are Some of the Uses of Brackets in Mathematics?
Brackets can be of various types such as parentheses, square and curly brackets. Using brackets helps to create groups and in order to gain more clarity about the order of the mathematical operations that are to be performed in an equation.
8. What is meant by the Place Value in the Number System?
The value that a digit represents on the basis of the position of the digit in a number is known as the place value of the digit. The place value can be tens, hundreds, thousands, and so on. For example, the place value of 9 in 2998 is hundreds and it represents the hundredth place. To learn more about the place value in detail, students can visit Vedantu.
9. What is meant by BODMAS?
BODMAS is an abbreviation for a bracket, orders, division, multiplication, addition, and subtraction. It is one of the most important rules in mathematics which is followed to do calculations in maths. It is according to this rule the sequence is followed while performing mathematical operations.
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How to Answer Case Study: few tips
Here are a few tips on how to answer questions relating to case studies;
1)Read the case-study carefully: Case-studies will run up to many lines. So, do not think twice about spending time on reading the question. Read it the second time if [o haven’t understood clearly.
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2)Read the questions relating to the case: After a first time reading of the case study, reading the questions pertaining to it, will help you know what to look out for in the case. Underline these instances in the case study for later reference.
3)Make notes of key points: While reading through your case study, make notes of key points (in bullet format).
This will help you to assess and analyses the facts for arriving at the right solution.
4)Look for cues: Sometimes, the answer may be hidden in the question itself. Certain Norms, or conjunctions in the sentence will give away the answer, if you read between them. Remember to look for these cues.
5)Background preparation: attempting case studies questions will be easier if you have enough exposure to solving these question types earlier.
Browse through detent portals or your university online interface to get better insights about case studies, and the mode to solve them.
Case studies are a vital part of testing management expertise and are woven into the distance learning MBA programs, which follow industry-standards. With the above tips, you can practice such type of questions with a new approach and get the expected results. Identification of issues ; problems There are three steps involved in the identification and analysis of issues and problems.
What are The Steps of Writing Content Analysis Case Study ?
Step 1 – overview of the case study (background context)
Understanding the background issues helps to understand the context of the case study. Read the case study to gain an overview and ask and answer the following questions as you read.
* What background facts influence the current problems? * What are the constraints or obstacles of the situation?
Step 2 – identifying the problems Identifying the major problems and their causes at this stage is vital to identify appropriate solutions later. Re-read the case study and summaries or list the issues and / or problems in your own words.
Make sure you: * sort he major problems from the minor problems * identify evidence from the case study which relates to each of the problems * identify underlying causes of the problems. A setup strategy is to represent the problems and their relationships as a mind.
Step 3 – linking theory to problems and case evidence Relating the identified issues / or problems to theory is vital when answering case studies.
This is where you demonstrate your knowledge of the theory in your course and your ability to relate it to practical situations.
If you are afraid to be expelled or think that you will not pass the plagiarism of your work, then it is better to ask for help in writing the case study with us.
Use your readings to select appropriate theories to match the identified problems. * Home * Identifying issues * Solutions * Recommendations I Antispasmodics can be a useful strategy to summaries / organism problems and to show their relationships to each other. The example below is a representation of the problems of the management case study.
Example I * Home * Identifying issues * Solutions * Recommendations I Integrating theory in a case strangulating relevant theory into your case study answer is vital. His allows you to demonstrate how theory relates to the actual issues / problems mound in the case study, as well as demonstrate your understanding of your course content. The following example shows how the theory and issues have been woven together. Example I * Home * Identifying issues * Solutions * Recommendations I Solution’s section evaluates potential solutions for the identified key problems. Often there is more than one solution, so it is useful to evaluate each solution in terms of its advantages and disadvantages.
This will also assist in determining your recommendations.
Things that may need to be considered are: * costs * time * sources * expertise. Structures section should be clear and concise. Recommended structure: * use headings and subheadings where possible * bullet points or numbered lists can also be used to list the advantages and disadvantages. Example I Recommendation’s section should outline your recommendations based upon the given solutions for each of the identified problems.
It may also need to include an action plan, egg what should be done by whom and the associated timeliness, but check with your teacher / lecturer for specific requirements.
Each recommendation would be realistic, ‘e practical and achievable, and be linked back to relevant and supporting theory. Structuralizes and subheadings should be used in this section. For example:communication * Staff constitutionalism the recommendations based on the identified solutions and supported by relevant theory. * Staff meetinghouse the recommendations based on the identified solutions and supported by relevant theory.
Leadership * Team bloodletting the theory. * Participative leadership storyline the recommendations based on the Identified solutions and supported by relevant theory. I
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CBSE Class 6 Maths Knowing Our Numbers Hots
Chapter 1 knowing our numbers class 6 mathematics hots.
Class 6 Mathematics students should refer to the following high order thinking skills questions with answers for Chapter 1 Knowing Our Numbers in standard 6. These HOTS questions with answers for Grade 6 Mathematics will come in exams and help you to score good marks
HOTS Questions Chapter 1 Knowing Our Numbers Class 6 Mathematics with Answers
1. The Greek mathematician, Archimedes, lived in the third century BC. He found the existing system of numbers very cumbersome to calculate with and wrote a book called ‘The Sand Reckoner’, in which he devised a method for forming large numbers. The Greek word for 10,000 was myriad. Archimedes started thinking of a myriad of myriads. Archimedes called this number an octade. a. What would we call a myriad of myriads according to the International and the Indian system? b. Archimedes called a number that had 1 followed by 16 zeros a second octade. How many zeros will follow 1 in myraid of second octade in Indian system of numeration? Answer: a. One hundred million or ten crore b. 1 followed by 20 zeros
2. Write each of the following quantities in numerals and in words (Indian system). Do not forget the leap years. a. The number of seconds in a leap year. b. The number of hours in the year 1900. c. The number of minutes in the year 2001. Answer: a. 31622400 seconds ; Three crore sixteen lakh twenty two thousand four hundred b. 8784 hrs. ; Eight thousand seven hundred eighty four c. 525600 min. ; Five lakh twenty five thousand six hundred
3. A certain 3 digit number, when rounded off the nearest hundreds gives 600, to the nearest tens gives 570. The sum of its digits is 18 and it is an odd number. What is thisa number? Answer: 567
4. Four cities A, B, C and D lie in a straight line on the East-West Highway. You have to discover the positions of these cities on the highway and answer the questions. City A is 20 km to the West of city D. City D is 50 km to the East of city C. City A is 70 km to the West of city B. a. What is the distance between city A and city C? b. Which city is at the eastern-most point? c. Which city is at the western-most point? d. What is the distance you would travel to go from the western-most point to the eastern-most point? Answer: a. 30 km b. City B c. City C d. 100 km
1. Form the largest number using the digits 9, 7, 5, 3, 1 each exactly twice. What is the smallest number you can write?
2. Form the largest number using the digits 1,2,3,4,5,6,7,8, each once, such that 5 and 2 are adjacent digits.
3. What is the largest number you can write such that the sum of its digits is 2? What is the smallest number you can write with the sum of the digits 2? (The sum of the digits of a number is called its digital sum.)
4. Prove that the largest 6-digit number with digital sum 50 is divisible by 5.
5. A student was asked to round off 12345 to its nearest hundred. He decided to round off first to the nearest 10 and wrote it as 12350. Since 50 is to be rounded off to 100, he next rounded off 12345 to the nearest 100 as 12400. But 12345 is nearer to 12300 than 12400. Why did he get the wrong answer?
6. What is the largest 8-digit number having distinct digits?
7. What is the largest number having 3 and 5 as its only digits, 3 appearing 3 times and 5 appearing 5 times, yet divisible by 5?
8. Is there the largest number having distinct digits? What is the smallest number having distinct digits?
9. Arrange the digits of 80096589432 to make the resulting number as large as possible. Arrange its digits such that the resulting number is as small as possible.
10. Find the value of 15!. How many digits are there in it? How many zeros are there at its end? (n! means you have to multiply all numbers from 1 to n. For example, 6! = 1 × 2 × 3 × 4 × 5 × 6 = 720.)
11. Find an 8-digit number formed using 2, 3, 4, 5, 6, 7, 8, 9, each once, such that the resulting number is divisible by 11. Can you find more such numbers?
12. What is the smallest 6-digit number which has 8 in its hundreds place and 6 in its lakhs place (digits may repeat)?
13. What is the smallest 8-digit number which has 7 in its lakh’s place, 4 in its thousand’s place, 3 in its ten’s place and having distinct digits? What is your answer if digits are allowed to repeat?
14. Suppose you take the digital sum of a number. You get another number. Take its digital sum, you get another number. Repeat this process till you get a single digit number. This single digit number is called the digital root of the given number. For example, the digital root of 9986 is 5. (9+9+8+6= 32 and 3+2=5.) Find the digital root of the number 1234567891011121314151617181920, the number obtained by writing 1 to 20 in a row.
15. What is the smallest number having at least 3 digits and having digital root 8?
16. Exploration : List all numbers from 1 to 200 whose digital root is 9. Are these divisible by 9? Check this property for numbers from 201 to 400. (The result is that a number is divisible by 9 if and only if its digital root is 9.)
1. Counting numbers 1, 2, 3.... are called natural numbers.
2. 1 is the smallest natural number.
3. There is no largest natural number.
4. Any number (however large) can be written by using ten symbols 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 called digits or figures.
5. The place value of a (non-zero) digit depends upon the place it occupies in the number; the place value of the digit 0 is always 0 regardless of the place it occupies in the number.
6. The face value of a digit in a number is the digit itself, regardless of the place it occupies in the number.
7. If a place is vacant in a number, put 0 at that place. Never put 0 at the extreme left of a number.
8. A single digit or a group of digits representing a number is called numeral.
9. Writing a number in words is called numeration.
10. To read and write numbers, the two systems of numeration in common use are : a. Indian system b. International system.
11. In the Indian system, the various periods from the right are: ones, thousands, lakhs, crores and so on. While in the International system, periods from the right are: ones, thousands, millions, billions and so on.
12. In the Indian system, the first comma comes after 3-digits, from the right and next comma comes after every 2-digits; while in the International system, the commas come after every 3-digits from the right.
13. 1 million = 10 lakh, 10 million = 1 crore, 100 million = 10 crore, 1 billion = 100 crore
14. Comparison of numbers. Given two numbers, the number having more digits is greater. If the number of digits is equal, then start comparing digits from the extreme left i.e. the highest place till we get a pair of unequal digits, the number having greater digit is greater.
15. 1 km = 1000 m, lm = 100 cm. 1 cm = 10 mm 1 kg = 1000 g, lg = 1000 mg 1 kL = 1000 L, 1L= 1000 mL
16. Estimation. To estimate (or round off) a number to the nearest a. Tens: i. If the digit at ones place is less than 5, then replace ones digit by 0 and keep all other digits as they are. ii. If the digit at ones place is 5 or greater than 5, then increase the tens digit by 1 and replace the ones digit by 0.
b. Hundreds: i. If the digit at tens place is less than 5, then replace each of the digits at tens place and ones place by 0. Keep all other digits as they are. ii. If the digit at tens place is 5 or greater than 5, then increase the digit at hundreds place by 1 and replace each of the digits at tens place and ones place by 0.
c. Thousands : i. If the digit at hundreds place is less than 5, then replace each of the digits at hundreds place, tens place and ones place by 0. Keep all other digits as they are. ii. If the digit at hundreds place is 5 or greater than 5, then increase the digit at thousands place by 1 and replace each of the digits at hundreds place, tens place and ones place by 0.
18. Certain basic rules to write any number in Roman numerals are: Rule 1. If a symbol is repeated, its value is added as many times as it occurs. a. Only symbols I, X, C and M can be repeated. b. A symbol can be repeated atmost three times. c. Symbols V, L and D are never repeated.
Rule 2. If a symbol of a smaller value is written to the right of a symbol of a greater value, then its value gets added to the value of the greater symbol.
Rule 3. If a symbol of a smaller value is written to the left of a symbol of a greater value, then its value gets subtracted from the value of the greater symbol. a. Symbols V, L and D are never written to the left of a symbol of a greater value. b. I can be subtracted from V and X only. c. X can be subtracted from L and C only. d. C can be subtracted from D and M only.
Rule 4. If a symbol of smaller value is written between two symbols of greater values, then its value is always subtracted from a symbol of the greater value which comes immediately after the symbol of the smaller value.
Rule 5. If a bar is placed over a symbol, then its value gets multiplied by 1000.
ERRORANALYSIS
1. Students write the place instead of the place value or period and vice versa.
2. While comparing, some times, instead of counting number of digits first, students start comparing the digit at the highest place.
3. While writing the number, students put commas at the wrong place.
4. While forming numbers, students put commas after every digit.
Using Flash Cards
ACTIVITY II
a. The number of mints is an odd three-digit number. b. The sum of the ones digit and the tens digit is one less than the hundreds digit. c. When distributed equally among ten children, 3 mints are left. d. The hundreds digit is 1 less than twice the ones digit. Hint : When any number is divided by 10, the remainder obtained is the ones digit. For example, 234 ÷ 10 leaves a remainder of 4. ANSWER Riddle 513
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Knowing Our Numbers: Definition, Types & Examples
Numbers contribute towards understanding which collection of objects is larger or smaller and further helps to arrange them in order. Counting items is easy for us now. Students can count objects in large numbers. For example, the number of students in the school, and represent them through numerals. It further helps in identifying large numbers using proper number names. Thousands of years ago, people knew only small numbers. Gradually, students will learn to deal with larger numbers. We use numbers in sequences, patterns and series. Let us learn more about numbers in detail in this article.
Numbers: Definition
Numbers are the values that we use for expressing the quantity and perform the calculations. We have the digits \(0,\;1,\;2,\;3,\;4,\;5,\;6,\;7,\;8,\;9\) to make all the other numbers.
NCERT Solutions for Knowing Our Numbers Chapter
What is Number System?
The number system is the writing system where we express a number using mathematical notation representing the numbers of a given set using the numbers or symbols. We can classify the numbers into different groups. Let us discuss it in brief.
Real Numbers
Rational numbers, whole numbers, natural numbers, large numbers.
We know that we could divide the numbers into tens, hundreds, thousands, lakhs, crore, etc. These are the place values of the numbers of the Indian number system. We could divide the numbers into tens, hundreds, thousands, millions, and billions in the international number system, etc. We start reading the number with the largest group on the left and work our way to the right side.
Indian System of Numbers
In this system, we divide the given numbers into groups. We start from the extreme right digit of the given number and move towards the left—the first three digits on the extreme right for a group of ones. We divide the digits in one column into hundreds, tens and units.
The second group of the next two digits on the left of the group of ones form the group of thousands. Further, we divide it into thousands and ten thousand. Then, the third group of the next two digits on the left of the group of thousands form the group of lakhs, which we divide into lakhs and ten lakhs. Then, two digits on the left of the group of lakhs form a group of crores which is split up into crores and ten crores.
Indian Place Value Chart
Example: The number \(25,64,547\) is read in the Indian system in words as Twenty-five lakhs sixty-four thousand five hundred and forty-seven.
International System of Numbers
The maximum countries follow the international system of numeration in the world. In this system also, a number is divided into groups or periods. We start from the extreme right digit of the number to form the groups. The groups are known as ones, thousands, millions, and billions.
The digits in one column are split into hundreds, tens and units. The second group of the next three digits on the left of the group of ones form the group of thousands. We could split up into thousands, ten thousand and hundred thousand. The third group of the next three digits on the left of the group of thousands creates millions. Finally, three digits on the left of the group of millions form billions, which is divided into billions, ten billion, and a hundred billion. It is presented below.
The International System of Numeration Chart
Example: We can read \(23,501,582\) in words as twenty-three million five hundred one thousand five hundred eighty-two.
Comparison of Numbers
Comparison is the method that says about the similar properties of different objects. The basic concept in mathematics helps us describe whether the numbers are equal, or one is greater than or one is smaller than the other, in comparing two numbers.
There are three special symbols used in a comparison of numbers. The basic symbols used in the comparison of numbers are given below:
1. Greater than \(\left( > \right)\) 2. Less than \(\left( < \right)\) 3. Equals to \(\left( = \right)\)
Using the above symbols, we can compare two numbers of any type, such as natural numbers, whole numbers, integers and decimal numbers etc. Thus, comparing and exploring the differences between the numbers is known as the comparison of numbers.
Methods for Comparison of Numbers
If two numbers with a different number of digits are given, and we need to select the greater number, we look at the number of digits and find the answer. Now, how do you compare \(4875\) and \(3542\)? These two numbers have the same number of digits. They are both in thousands. But the digit at the thousands place in \(4875\) is greater than that in \(3542.\) Therefore, \(4875\) is greater than \(3542.\)
Next, tell which is greater, \(4875\) or \(4542\)? Here, too the numbers have the same number of digits. Further, the digits at the thousands place are the same in both. What do we do then? We move to the next digit, that is, the digit at the hundreds place. The digit at the hundred places is greater in \(4875\) than in \(4542.\)
Therefore, \(4875\) is greater than \(4542.\) If the hundreds place is the same in two numbers, then we need to compare the tens place and so on. Let us compare the numbers \(572\) and \(518.\) Here, given numbers have the same number of digits, and the left-most digit \(\left( 5 \right)\) is the same. So, next, we need to compare the following number towards the right, such as \(\left( 7 \right)\) and \(\left( 1 \right)\)
So, \(572\) is the greater number.
Solved Examples – Knowing Our Numbers
Q.1. Write the expanded form of the numbers \(375\) and \(921.\) Ans: Given the numbers \(375\) and \(921.\) You need to express the given numbers in the expanded form. Now, \(375 = 300 + 70 + 5\) So, the number \(921\) in which the digit \(9\) is in the hundreds place, \(2\) is in the tens place, \(1\) is in the ones place. So, \(921 = 900 + 20 + 1\) Hence, the required answer is \(375\) is \(300 + 70 + 5\) and \(921\) is \(900 + 20 + 1.\)
Q.2.Find the sum of the greatest two-digit number and the smallest three-digit number. Ans: We know that the greatest two-digit number is \(99.\) The smallest three-digit number is \(100.\) Now, \(99 + 100\) \( = 199\) Hence, the required answer is \(199.\)
Q. 3. Write the given numbers in words using the Indian system. \(830,154.\) Ans: Given to write the given numbers in words \(830,154.\) Here, the number name of \(830\) is Eight Hundred Thirty. The number name of \(154\) is One Hundred Fifty-Four.
Q.4. Write the given number in words in the International System: \(15,314,103.\) Ans: Given number is \(15,314,103.\) So, you read the number \(15,314,103\) as fifteen million three-fourteen hundred thousand one hundred and three.
Q.5. Identify the greater number from the following. \(2561,3524\) Ans: Given \(2561,3524.\) These two numbers have the same number of digits. They are both in thousands. But the digit at the thousands place in \(3524\) is greater than that in \(2561.\) Therefore, \(3524\) is greater than \(2561.\)
In the given article, the topics covered are about the various types of numbers. Then, we discussed the properties of numbers. Also, we learned the number names, which includes both Indian systems, international system of numbers, place value. At last, we discussed a few solved examples for a better understanding.
Learn All the Concepts on Number System
Frequently Asked Questions (FAQs) – Knowing Our Numbers
Frequently asked questions related to numbers are listed as follows:
Q.1. What are types of numbers? Ans: We can classify the numbers into different groups. The types of numbers are real numbers, imaginary numbers, whole numbers, natural numbers, integers, decimals, fractions, rational numbers, irrational numbers, etc.
Q.2. Which is the greatest number? Ans: The greatest number is not possible to identify if the range of the numbers is not given as there are infinite numbers.
Q.3. What is the number system in maths? Ans: The number system is the writing system where we express a number using mathematical notation representing the numbers of a given set using the numbers or symbols.
Q.4. What do you understand by numbers? Ans: Numbers are the values that we use for expressing the quantity and perform the calculations. We have the digits \({\text{0,1,2,3,4,5,6,7,8,9}}\) to make all the other numbers.
Q.5. How do you read a number? Ans: When you are reading a number, you have to begin at the left with the largest group and proceed to the right. For example, \(675\) is read as six hundred and seventy-five.
We hope this detailed article on the concept of knowing our numbers helped you in your studies. If you have any doubts, queries or suggestions regarding this article, feel free to ask us in the comment section and we will be more than happy to assist you. Happy learning!
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- NCERT Solutions
- NCERT Class 6
- NCERT 6 Maths
- Chapter 1: Knowing Our Numbers
NCERT Solutions for Class 6 Maths Chapter 1: Knowing Our Numbers
NCERT Solutions for Class 6 Maths Chapter 1 Knowing Our Numbers help the students who aspire to obtain good academic score in exams. Experts at BYJU’S designed these solutions to boost the confidence of students by assisting them in understanding the concepts covered in this chapter. NCERT Solutions for Class 6 contains the methods to solve problems present in the textbook quickly and easily. These materials are prepared based on the Class 6 NCERT syllabus, taking the types of questions asked in the NCERT textbook into consideration.
Utilising the NCERT Solutions will aid students in understanding the key concepts effortlessly. Further, all the solutions are in accordance with the latest CBSE guidelines and marking schemes. Download the solutions of this chapter in PDF format from the link attached below to kickstart preparations.
- Chapter 1 Knowing Our Numbers
- Chapter 2 Whole Numbers
- Chapter 3 Playing with Numbers
- Chapter 4 Basic Geometrical Ideas
- Chapter 5 Understanding Elementary Shapes
- Chapter 6 Integers
- Chapter 7 Fractions
- Chapter 8 Decimals
- Chapter 9 Data Handling
- Chapter 10 Mensuration
- Chapter 11 Algebra
- Chapter 12 Ratio and Proportion
- Chapter 13 Introduction to Symmetry
- Chapter 14 Practical Geometry
- Exercise 1.1 Chapter 1 Knowing Our Numbers
- Exercise 1.2 Chapter 1 Knowing Our Numbers
- Exercise 1.3 Chapter 1 Knowing Our Numbers
NCERT Solutions for Class 6 Chapter 1: Knowing Our Numbers Download PDF
Access NCERT Solutions for Class 6 Chapter 1: Knowing Our Numbers
Exercise 1.1 PAGE NO: 12
1. Fill in the blanks:
(a) 1 lakh = ………….. ten thousand.
(b) 1 million = ………… hundred thousand.
(c) 1 crore = ………… ten lakhs.
(d) 1 crore = ………… million.
(e) 1 million = ………… lakhs.
(a) 1 lakh = 10 ten thousand
(b) 1 million = 10 hundred thousand
= 10,00,000
(c) 1 crore = 10 ten lakhs
= 1,00,00,000
(d) 1 crore = 10 million
(e) 1 million = 10 lakhs
= 1,000,000
2. Place commas correctly and write the numerals:
(a) Seventy three lakh seventy five thousand three hundred seven
(b) Nine crore five lakh forty one
(c) Seven crore fifty two lakh twenty one thousand three hundred two
(d) Fifty eight million four hundred twenty three thousand two hundred two
(e) Twenty three lakh thirty thousand ten
(a) The numeral of seventy three lakh seventy five thousand three hundred seven is 73,75,307
(b) The numeral of nine crore five lakh forty one is 9,05,00,041
(c) The numeral of seven crore fifty two lakh twenty one thousand three hundred two is 7,52,21,302
(d) The numeral of fifty eight million four hundred twenty three thousand two hundred two is 5,84,23,202
(e) The numeral of twenty three lakh thirty thousand ten is 23,30,010
3. Insert commas suitably and write the names according to the Indian System of Numeration:
(a) 87595762 (b) 8546283 (c) 99900046 (d) 98432701
(a) 8,75,95,762 – Eight crore seventy five lakh ninety five thousand seven hundred sixty two
(b) 85,46,283 – Eighty five lakh forty six thousand two hundred eighty three
(c) 9,99,00,046 – Nine crore ninety nine lakh forty six
(d) 9,84,32,701 – Nine crore eighty four lakh thirty two thousand seven hundred one
4. Insert commas suitably and write the names according to the International System of Numeration:
(a) 78921092 (b) 7452283 (c) 99985102 (d) 48049831
(a) 78,921,092 – Seventy eight million nine hundred twenty one thousand ninety two
(b) 7,452,283 – Seven million four hundred fifty-two thousand two hundred eighty three
(c) 99,985,102 – Ninety-nine million nine hundred eighty five thousand one hundred two
(d) 48,049,831 – Forty-eight million forty-nine thousand eight hundred thirty-one
Exercise 1.2 PAGE NO: 16
1. A book exhibition was held for four days in a school. The number of tickets sold at the counter on the first, second, third and final day was respectively 1094, 1812, 2050 and 2751. Find the total number of tickets sold on all four days.
Number of tickets sold on 1st day = 1094
Number of tickets sold on 2nd day = 1812
Number of tickets sold on 3rd day = 2050
Number of tickets sold on 4th day = 2751
Hence, the total number of tickets sold on all four days = 1094 + 1812 + 2050 + 2751 = 7707 tickets
2. Shekhar is a famous cricket player. He has so far scored 6980 runs in test matches. He wishes to complete 10,000 runs. How many more runs does he need?
Shekhar scored = 6980 runs
He wants to complete = 10000 runs
Runs needed to score more = 10000 – 6980 = 3020
Hence, he needs 3020 more runs to score
3. In an election, the successful candidate registered 5,77,500 votes, and his nearest rival secured 3,48,700 votes. By what margin did the successful candidate win the election?
No. of votes secured by the successful candidate = 577500
No. of votes secured by his rival = 348700
Margin by which he won the election = 577500 – 348700 = 228800 votes
∴ The successful candidate won the election by 228800 votes
4. Kirti bookstore sold books worth Rs 2,85,891 in the first week of June and books worth Rs 4,00,768 in the second week of the month. How much was the sale for the two weeks together? In which week was the sale greater and by how much?
Price of books sold in the first week of June = Rs 285891
Price of books sold in the second week of June = Rs 400768
No. of books sold in both weeks together = Rs 285891 + Rs 400768 = Rs 686659
The sale of books is the highest in the second week.
Difference in the sale in both weeks = Rs 400768 – Rs 285891 = Rs 114877
∴ Sale in the second week was greater by Rs 114877 than in the first week.
5. Find the difference between the greatest and the least 5-digit number that can be written using the digits 6, 2, 7, 4, and 3 each only once.
Digits given are 6, 2, 7, 4, 3
Greatest 5-digit number = 76432
Least 5-digit number = 23467
Difference between the two numbers = 76432 – 23467 = 52965
∴ The difference between the two numbers is 52965.
6. A machine, on average, manufactures 2,825 screws a day. How many screws did it produce in the month of January 2006?
Number of screws manufactured in a day = 2825
Since January month has 31 days,
The number of screws manufactured in January = 31 × 2825 = 87575
Hence, the machine produced 87575 screws in the month of January 2006.
7. A merchant had Rs 78,592 with her. She placed an order for purchasing 40 radio sets at Rs 1200 each. How much money will remain with her after the purchase?
Total money the merchant had = Rs 78592
The number of radio sets she placed an order for purchasing = 40 radio sets
Cost of each radio set = Rs 1200
So, cost of 40 radio sets = Rs 1200 × 40 = Rs 48000
Money left with the merchant = Rs 78592 – Rs 48000 = Rs 30592
Hence, money left with the merchant after purchasing radio sets is Rs 30592.
8. A student multiplied 7236 by 65 instead of multiplying by 56. By how much was his answer greater than the correct answer?
Difference between 65 and 56, i.e. (65 – 56) = 9
The difference between the correct and incorrect answer = 7236 × 9 = 65124
Hence, by 65124, the answer was greater than the correct answer.
9. To stitch a shirt, 2 m 15 cm cloth is needed. Out of 40 m cloth, how many shirts can be stitched and how much cloth will remain?
The total length of the cloth = 40 m
= 40 × 100 cm = 4000 cm
Cloth required to stitch one shirt = 2 m 15 cm
= 2 × 100 + 15 cm = 215 cm
Number of shirts that can be stitched out of 4000 cm = 4000/215 = 18 shirts
Hence, 18 shirts can be stitched out of 40 m, and 1 m 30 cm of cloth is left.
10. Medicine is packed in boxes, each weighing 4 kg 500g. How many such boxes can be loaded in a van which cannot carry beyond 800 kg?
Weight of one box = 4 kg 500 g = 4 × 1000 + 500
Maximum weight carried by the van = 800 kg = 800 × 1000
Hence, the number of boxes that can be loaded in the van = 800000/4500 = 177 boxes
11. The distance between the school and a student’s house is 1 km 875 m. Every day, she walks both ways. Find the total distance covered by her in six days.
Distance covered between the school and her house = 1 km 875 m = 1000 + 875 = 1875 m
Since the student walks both ways,
The distance travelled by the student in one day = 2 × 1875 = 3750 m
Distance travelled by the student in 6 days = 3750 m × 6 = 22500 m = 22 km 500 m
∴ The total distance covered by the student in six days is 22 km and 500 m.
12. A vessel has 4 litres and 500 ml of curd. In how many glasses, each of 25 ml capacity, can it be filled?
Quantity of curd in the vessel = 4 l 500 ml = 4 × 1000 + 500 = 4500 ml
Capacity of 1 glass = 25 ml
∴ Number of glasses that can be filled with curd = 4500 / 25 = 180 glasses
Hence, 180 glasses can be filled with curd.
Exercise 1.3 Page NO: 23
1. Estimate each of the following using the general rule:
(a) 730 + 998 (b) 796 – 314 (c) 12904 + 2888 (d) 28292 – 21496
Make ten more such examples of addition, subtraction and estimation of their outcome.
(a) 730 + 998
Round off to hundreds
730 rounds off to 700
998 rounds off to 1000
Hence, 730 + 998 = 700 + 1000 = 1700
(b) 796 – 314
796 rounds off to 800
314 rounds off to 300
Hence, 796 – 314 = 800 – 300 = 500
(c) 12904 + 2888
Round off to thousands
12904 rounds off to 13000
2888 rounds off to 3000
Hence, 12904 + 2888 = 13000 + 3000 = 16000
(d) 28292 – 21496
28292 round off to 28000
21496 round off to 21000
Hence, 28292 – 21496 = 28000 – 21000 = 7000
Ten more such examples are
(i) 330 + 280 = 300 + 300 = 600
(ii) 3937 + 5990 = 4000 + 6000 = 10000
(iii) 6392 – 3772 = 6000 – 4000 = 2000
(iv) 5440 – 2972 = 5000 – 3000 = 2000
(v) 2175 + 1206 = 2000 + 1000 = 3000
(vi) 1110 – 1292 = 1000 – 1000 = 0
(vii) 910 + 575 = 900 + 600 = 1500
(viii) 6400 – 4900 = 6000 – 5000 = 1000
(ix) 3731 + 1300 = 4000 + 1000 = 5000
(x) 6485 – 4319 = 6000 – 4000 = 2000
2. Give a rough estimate (by rounding off to the nearest hundreds) and also a closer estimate (by rounding off to the nearest tens):
(a) 439 + 334 + 4317 (b) 108734 – 47599 (c) 8325 – 491 (d) 489348 – 48365
Make four more such examples.
(a) 439 + 334 + 4317
Rounding off to the nearest hundreds
439 + 334 + 4317 = 400 + 300 + 4300
Rounding off to the nearest tens
439 + 334 + 4317 = 440 + 330 + 4320
(b) 108734 – 47599
108734 – 47599 = 108700 – 47600
108734 – 47599 = 108730 – 47600
(c) 8325 – 491
8325 – 491 = 8300 – 500
8325 – 491 = 8330 – 490
(d) 489348 – 48365
489348 – 48365 = 489300 – 48400
489348 – 48365 = 489350 – 48370
Four more examples are as follows:
(i) 4853 + 662
4853 + 662 = 4800 + 700
4853 + 662 = 4850 + 660
(ii) 775 – 390
775 – 390 = 800 – 400
775 – 390 = 780 – 400
(iii) 6375 – 2875
6375 – 2875 = 6400 – 2900
6375 – 2875 = 6380 – 2880
(iv) 8246 – 6312
8246 – 6312 = 8200 – 6300
8246 – 6312 = 8240 – 6310
3. Estimate the following products using the general rule:
(a) 578 × 161
(b) 5281 × 3491
(c) 1291 × 592
(d) 9250 × 29
Rounding off by general rule
578 and 161 rounded off to 600 and 200, respectively
____________
_____________
5281 and 3491 rounded off to 5000 and 3500, respectively
1291 and 592 rounded off to 1300 and 600, respectively
______________
9250 and 29 rounded off to 9000 and 30, respectively
Disclaimer:
Dropped Topics – 1.3.1 Estimation, 1.3.2 Estimating to the nearest tens by rounding off, 1.3.3 Estimating to the nearest hundreds by rounding off, 1.3.4 Estimating to the nearest thousands by rounding off, 1.3.5 Estimating outcomes of number situations, 1.3.6 To estimate sum or difference, 1.3.7 To estimate products, 1.4 Using brackets, 1.4.1 Expanding brackets, 1.5 Roman numerals.
Frequently Asked Questions on NCERT Solutions for Class 6 Maths Chapter 1
What are the topics covered in chapter 1 of ncert solutions for class 6 maths, how many problems are there in each exercise of ncert solutions for class 6 maths chapter 1, what does chapter 1 of ncert solutions for class 6 maths convey.
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How to answer case study questions.
A case study examination is composed of a set of questions surrounding a single problem, person, place or thing. Each problem attacks different angles of the subject matter to determine if the examinee comprehends the particular problem(s) and can solve them. Case study examinations can be used in business, technology, medicine, psychology, advertising, law, consulting and science. The questions are ideal for testing the knowledge of an individual who must prove his grasp of the subject matter in a particular field, i.e., the legal professional.
A week or two before the case study, locate a practice test and run through it a few times on your own. The more acquainted you are with the word arrangement of this type of test, the more comfortable you will be during either a written or oral case study assessment.
On the day of the case study test, relax and allow yourself to remember what you have learned from previous readings on the subject. You should possess a wealth of knowledge in this area from classes you have taken or work experience. Just use what you already know to answer the questions.
To answer questions on a case study examination in the best possible way, read or listen for the topic sentence. This is usually the first sentence in the introduction or first paragraph. This sentence presents the problem and thus holds key information; it tells you what the problem is about. Make sure that you understand the topic before reading the case study.
Next, read or focus on the meaning of the entire study question to become familiar with the nature and scope of the problem. Go over it again more slowly, a second time, if you do not understand it during the first read. Do not skip, skim or gloss over the content. Otherwise, vital information that you will need to answer the question might be missed. Note word arrangement, facts, figures or statistics in the text that will help come up with a solution. Think of different ways that you can answer the case study question and then determine the effects of each answer on your outcome.
Visualize the scenario or situation posed by the question. See it in your mind's eye as you review it. Consider the question as if it were an actual problem that will affect the lives of others. Write the best possible answer.
Slow down if you start to get confused. You may be moving too fast, trying to beat the clock. If this is the case, answer the easiest questions first and come back to the harder ones later. This will buy you some time and hopefully boost your confidence enough for you to calm down and can answer the more difficult questions with less anxiety.
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Juanita King began writing in 1971. She holds a master's degree in written communication and a master's degree in human development with a post-master's degree in counseling from National-Louis University.
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- Multiple Choice Questions
- Knowing Our Numbers
Knowing Our Numbers Multiple Choice Questions (MCQ’s)
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Instructions
- Keep paper and pencil ready but keep your books away.
- Click the "Begin Test" button to start the test.
- You can move between questions and answer them in any order you like.
- Click on "End Test" when you are done.
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- You will be able to view the solutions only after you end the test.
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Grade 6 / Case Study 2 AT 4 SATE AANCE PEOANCE TAS Item 3 Your teacher wants to use a point system to select the winning pet. She wants each pet to get a certain number of points for each 1st choice vote and a certain number of points for each 2nd choice vote. Your teacher decides to use these rules for her point system:
Knowing Our Numbers Class 6 Extra Questions Very Short Answer Type Question 1. Write the smallest three digit number whose value does not change on reversing its digits. Solution: The required number is 101. Question 2. Write the greatest three digit number which does not change on reversing its digits. Solution: The required number is 999.
These kinds of case study questions will highlight the business' need they had to fulfill and appeal to future clients. What was your team's process prior to using our product? This will give the reader a baseline to compare the results for your company's product. Were there any costs associated with the process prior to using our product?
Study Important Questions for Class 6 Mathematics Chapter 1 Knowing Our Numbers Very Short Answer Questions (1 Mark) 1. Write the numeration for 80956124 in the Indian system. Ans: The numeration for 80956124 in the Indian system is, 8, 09, 56, 124. Eight crore nine lakh fifty-six thousand one hundred twenty-four. 2.
Ch - 1 Knowing our Numbers Answer 10000000, 10000001, 10000002, 10000003, 10000004 Explanation: The smallest 8-digit number is 1,00,00,000 and the next four numbers are 1,00,00,001, 1,00,00,002, 1,00,00,003 and 1,00,00,004 24657 Explanation: The number has 4 in thousands place and 6 in hundreds place 78,921,092 1410 Explanation: 567 + 843 = 1410
A case study is an in-depth study of one person, group, or event. In a case study, nearly every aspect of the subject's life and history is analyzed to seek patterns and causes of behavior. Case studies can be used in various fields, including psychology, medicine, education, anthropology, political science, and social work.
done Knowing our Numbers Total Questions - 55 question_answer 1) Observe the following pattern for obtaining the sums, and find the sum of numbers from 781 to 790. A) 7055 B) 7855 C) 7955 D) 8155 View Solution play_arrow question_answer 2) In numbers from 1 to 100, how many times does the digit 0 appear? A) 9 B) 10 C) 11 D) 12
3. An industry-relevant question. SaaS tools that help with ad management may ask clients about their total monthly ad spend, for example. An eco-friendly company may ask clients what their "green goals" are or their previous carbon emissions. Think about what would benefit you to have in the case study, and ask it here if possible.
Q1) Arrange the numbers in increasing order 254, 87, 562 , 32564, 4581, 98778, 45, 12365, 456217. Q2) Find the estimate product of 206 x 789. Q3) Find the value of 27 x 104. Q4) Write the following numbers in Roman numeral: 45,12, 32, 89 ,100. Q5) Write the predecessor and successor of the following number: 1236, 789, 5474, 32658, 45789.
Important Questions for Class 6 Maths Knowing our Numbers In this page we have Important Questions for Class 6 Maths Knowing our Numbers Question 1 Solve the followings: 5(5−3) 5 ( 5 − 3) 20(40−32) 20 ( 40 − 32) (11+20)(31+30) ( 11 + 20) ( 31 + 30) (1 +6)+10 ( 1 + 6) + 10 2 ×(1 +3)(10+12)×(8 +6) 2 × ( 1 + 3) ( 10 + 12) × ( 8 + 6) Question 2
Round whole numbers Get 5 of 7 questions to level up! Estimating sum, difference, or product Learn Estimating adding and subtracting 3-digit numbers Multiplication estimation example Practice Estimate to add multi-digit whole numbers Get 3 of 4 questions to level up! Estimate multi-digit multiplication problems Get 3 of 4 questions to level up!
A reputed Case Study Sample Free online service provider will always be an excellent help for you in qualifying and getting good grades in your case study question sessions. In this blog, we will discuss the best ways to answer the case study questions on various topics and companies. How to Answer the Case Study Question? The case study ...
Explore numerous MCQ Questions of Knowing Our Numbers Class 6 with answers provided with detailed solutions by looking below. Question 1. The smallest 8 digit number is called (a) Ten lakh (b) One lakh (c) Ten crore (d) One crore Answer Question 2. Which of the following is not a symbol to write Roman numerals? (a) D (b) V (c) M (d) N Answer
a. What fundamental ideas (content) about number and operations is the teacher trying to teach? b. What mathematical processes does the teacher expect students to demonstrate? c. How do students demonstrate their knowledge of the intended content? What does the teacher do to elicit student thinking? Video Segment
Published on May 8, 2019 by Shona McCombes . Revised on January 30, 2023. A case study is a detailed study of a specific subject, such as a person, group, place, event, organization, or phenomenon. Case studies are commonly used in social, educational, clinical, and business research. A case study research design usually involves qualitative ...
The subtopics of comparing numbers are: How many numbers can you make? In this part, students will learn how they can make numbers from given digits. Numbers will be formed in such a way that no digit is repeated in a single number and there cannot be two exact numbers.
Here are a few tips on how to answer questions relating to case studies; 1)Read the case-study carefully: Case-studies will run up to many lines. So, do not think twice about spending time on reading the question. Read it the second time if [o haven't understood clearly. We Will Write a Custom Case Study Specifically. For You For Only $13.90 ...
NCERT Solution for Class 6 math - knowing our numbers 12 , Question 3 Page No 12: Question 4: Insert commas suitably and write the names according to International System of Numeration: (a). 78921092 (b). 7452283 (c). 99985102 (d). 48049831 Answer: (a) 78,921,092 Seventy eight million nine hundred twenty one thousand ninety two (b) 7,452,283
Class 6 Mathematics students should refer to the following high order thinking skills questions with answers for Chapter 1 Knowing Our Numbers in standard 6. These HOTS questions with answers for Grade 6 Mathematics will come in exams and help you to score good marks HOTS Questions Chapter 1 Knowing Our Numbers Class 6 Mathematics with Answers HOTS
Learn All the Concepts on Number System. Frequently Asked Questions (FAQs) - Knowing Our Numbers. Frequently asked questions related to numbers are listed as follows: Q.1. What are types of numbers? Ans: We can classify the numbers into different groups. The types of numbers are real numbers, imaginary numbers, whole numbers, natural numbers ...
Find the total number of tickets sold on all four days. Solutions: Number of tickets sold on 1st day = 1094 Number of tickets sold on 2nd day = 1812 Number of tickets sold on 3rd day = 2050 Number of tickets sold on 4th day = 2751 Hence, the total number of tickets sold on all four days = 1094 + 1812 + 2050 + 2751 = 7707 tickets 2.
To answer questions on a case study examination in the best possible way, read or listen for the topic sentence. This is usually the first sentence in the introduction or first paragraph. This sentence presents the problem and thus holds key information; it tells you what the problem is about. Make sure that you understand the topic before ...
Get MCQ Questions for Class 6 Maths Knowing Our Numbers on all the topics for free. Visit TopperLearning today to get complete access to Class 6 Maths Chapter 1 MCQ Questions!