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NCERT Solutions for Class 6 Maths Chapter 1 - Knowing Our Numbers

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NCERT Solutions for Class 6 Maths Chapter 1 - Knowing Our Numbers

Chapter 1 of the class 6 maths syllabus is on ‘Knowing Our Numbers’. This is a very important chapter in class 6 that develops a student’s number sense. This crucial chapter in the class 6 maths syllabus is divided into 5 major sections or topics. The following is a list of the important topics covered under NCERT Solutions for Class 6 Maths Chapter 1 - Knowing Our Numbers. We recommend that students carefully read through each one of these topics to get a clear understanding of the concepts introduced in the chapter and be able to utilize the provided solutions appropriately and efficiently.

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Table of Content
1. NCERT Solutions for Class 6 Maths Chapter 1 - Knowing Our Numbers
2. Glance on NCERT Solutions for Class 6 Maths Chapter 1
3. Access NCERT Solutions for Class 6 Maths Chapter 1- Knowing Our Numbers
4. Practice and Master the Concepts of the Chapter Knowing Our Numbers Class 6 Maths Chapter 1
    4.11.1 Introduction
    4.21.2 Comparing Numbers
    4.31.3 Large Numbers in Practice
    4.41.4 Using Brackets
    4.51.5 Roman Numerals
5. Overview of Deleted Syllabus for CBSE Class 6 Maths Chapter 1 Knowing Our Numbers 2024-25
6. Exercises of Class 6 Maths Chapter 1 Knowing Our Numbers
7. Other Study Material for CBSE Class 6 Maths Chapter 1
8. Chapter wise NCERT Solutions for Class 6 Maths
FAQs


Vedantu’s expert teachers have meticulously curated these solutions for the betterment of clarity in internalizing the concepts included in this chapter and to ensure that students are able to score well in exams easily after going through and practicing these solutions.


Glance on NCERT Solutions for Class 6 Maths Chapter 1

  • Chapter 1 of Class 6 Maths, "Knowing Our Numbers," focuses on strengthening your understanding of numbers and their basic operations.

  • Revisit the concept of numbers and how they help us count and measure things around us.

  • Comparing Numbers dives into techniques for comparing numbers. You'll learn how to identify the greater and smaller number, along with using symbols like '<' (less than) and '>' (greater than).

  • Place Value System is an important concept that deals with the value of a digit based on its position in a number. 

  • We will polishes your skill of reading and writing larger numbers, potentially up to six digits. Also learn about using commas to separate groups of digits for better readability (e.g., 1,234).

  • Practice arranging numbers in ascending order (smallest to biggest) and descending order (biggest to smallest).

  • There are three exercises (16 fully solved questions) in class 6th maths chapter 1 Knowing Our Numbers.


S.No.

Current Syllabus Exercise of  Class 6 Maths Chapter 1

1

NCERT Solutions of Class 6 Maths Knowing Our Numbers Exercise 1.1

2

NCERT Solutions of Class 6 Maths Knowing Our Numbers Exercise 1.2

3

NCERT Solutions of Class 6 Maths Knowing Our Numbers Exercise 1.3

4

NCERT Solutions of Class 6 Maths Knowing Our Numbers Exercise 1.4

5

NCERT Solutions of Class 6 Maths Knowing Our Numbers Exercise 1.6

6

NCERT Solutions of Class 6 Maths Knowing Our Numbers Exercise 1.6

Access NCERT Solutions for Class 6 Maths Chapter 1- Knowing Our Numbers

Exercise 1.1

1. Fill in the blanks:

(a) 1 lakh = ____ ten thousand

(b) 1 million =____ hundred thousand

(c) 1 crore = ____ ten lakh

(d) 1 crore =____ million

(e) 1 million = ____ lakh

Ans:

(a) 1 lakh = \[10\] ten thousand

(b) 1 million = \[10\] hundred thousand

(c) 1 crore =  \[10\] ten lakh

(d) 1 crore = \[10\] million

(e) 1 million =  \[10\] lakh


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.

Ans:

(a) Seventy-three lakh seventy-five thousand three hundred seven  \[=\text{ }73,75,307\text{ }\]

(b) Nine crore five lakh forty-one \[=\text{ }9,05,00,041\]

(c) Seven crore fifty-two lakh twenty-one thousand three hundred two \[=\text{ }7,52,21,302\text{ }\]

(d) Fifty-eight million four hundred twenty-three thousand two hundred two \[=\text{ }58,423,202\]

(e) Twenty-three lakh thirty thousand ten \[=\text{ }23,30,010\]


3. Insert commas suitable and write the names according to Indian system of numeration: 

(a) 87595762

(b) 8546283

(c) 99900046

(d) 98432701

Ans:

(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 suitable and write the names according to International system of numeration:

(a) 78921092

(b) 7452283

(c) 99985102

(d) 48049831

Ans:

(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

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 \[\mathbf{1094},\mathbf{1812},\mathbf{2050}\text{ }\mathbf{and}\text{ }\mathbf{2751}\]. Find the total number of tickets sold on all the four days.

Ans:

Tickets sold of first day \[=\text{ }1,094\]

Tickets sold of second day \[=\text{ }1,812\]

Tickets sold of third day = 2,050

Tickets sold of fourth day \[=~2,751\]

Total tickets sold \[\begin{align} & =\text{ }1,094+1,812+2,050+2,751 \\ & =\text{ }7,707 \\ \end{align}\]


2. Shekhar is a famous cricket player. He has so far scored \[\mathbf{6980}\] runs in test matches. He wishes to complete \[\mathbf{10},\mathbf{000}\] runs. How many more runs does he need?

Ans:

Runs scored by Shekhar \[=\text{ }6980\]

Total number of runs he need \[\begin{align} & =\text{ }10,000-6980 \\ & =\text{ }3020 \\ \end{align}\].


3. In an election, the successful candidate registered \[\mathbf{5},\mathbf{77},\mathbf{500}\] votes and his nearest rival secured \[\mathbf{3},\mathbf{48},\mathbf{700}\] votes. By what margin did the successful candidate win the election?

Ans: Successful candidate secured votes \[=\text{ }5,77,500\]

Rival candidate secured votes \[=\text{ }3,48,700\]

Margin of votes \[\begin{align} & =\text{ }5,77,500-3,48,700 \\ & =\text{ }2,28,800 \\ \end{align}\]


4. Kirti Bookstore sold books worth \[\mathbf{2},\mathbf{85},\mathbf{891}\] in the first week of June and books worth \[\mathbf{4},\mathbf{00},\mathbf{768}\] 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?

Ans: Books sold in week one \[=\text{ }2,85,891\]

Books sold in week second \[=\text{ }4,00,768\]

Total sale \[=\text{ }4,00,768+2,85,891=6,86,659\]

Clearly, sale of second week is more than the first week sale

Difference \[\begin{align} & =\text{ }4,00,768-2,85,891 \\ & =\text{ }1,14,877 \\ \end{align}\]


5. Find the difference between the greatest and the least number that can be written using the digits \[\mathbf{6},\mathbf{2},\mathbf{7},\mathbf{4},\mathbf{3}\] each only once.

Ans: Largest five digit number  \[=76432\]

Smallest five-digit number  \[=\text{ }23467\]

Therefore, the difference between then  \[\begin{align} & =\text{ }76432-23467 \\ & =\text{ }52965 \\ \end{align}\]


6. A machine, on an average, manufactures \[\mathbf{2},\mathbf{825}\]screws a day. How many screws did it produce in the month of January \[\mathrm{2006}\]?

Ans:

Screws produced in one day \[=\text{ }2,825\]

Total Screws produced in \[31\] days \[\begin{align} & =\text{ }2,825\times 31\text{ } \\ & =\text{ }87,575 \\ \end{align}\]

Hence, the machine produced \[87,575\] screws in the month of January.


7. A merchant had \[\mathbf{78},\mathbf{592}\]with her. She placed an order for purchasing \[\mathbf{40}\] radio sets at \[\mathbf{1},\mathbf{200}\] each. How much money will remain with her after the purchase?

Ans:

Total money merchant had \[=\text{ }Rs.\text{ }78,592\]

Cost of one radio \[=\text{ }Rs.\text{ }1200\]

Cost of \[40\] radios \[=\text{ }1200\times 40=\text{ }Rs.\text{ }48,000\]

Money left\[\begin{align} & =\text{ }78,592-48,000 \\ & =\text{ }30,592 \\ \end{align}\]


8. A student multiplied \[\mathbf{7236}\text{ }\mathbf{by}\text{ }\mathbf{65}\] instead of multiplying \[\mathbf{by}\text{ }\mathbf{56}\]. By how much was his answer greater than the correct answer?

Ans:

Wrong answer \[\begin{align} & =\text{ }7236\times 65\text{ } \\ & =\text{ }470340 \\ \end{align}\]

Correct answer \[\begin{align} & =\text{ }7236\times 56\text{ } \\ & =\text{ }405216 \\ \end{align}\]

Difference in answers \[\begin{align} & =\text{ }470340-405216\text{ } \\ & =\text{ }65,124 \\ \end{align}\]


9. To stitch a shirt \[\mathbf{2}\text{ }\mathbf{m}\text{ }\mathbf{15}\text{ }\mathbf{cm}\] cloth is needed. Out of \[\mathbf{40}\text{ }\mathbf{m}\] cloth, how many shirts can be stitched and how much cloth will remain?

Ans:

Cloth required for stitch one shirt 

\[\begin{align} & =\text{ }2\text{ }m\text{ }15\text{ }cm \\ & =\text{ }2\times 100\text{ }cm+15\text{ }cm \\ & =215cm \\ \end{align}\]

Total length of cloth \[\begin{align} & =\text{ }40\text{ }m\text{ } \\ & =\text{ }40\times 100\text{ }cm \\ & =4000\text{ }cm \\ \end{align}\]

Number of shirts that can be stitched = \[\frac{4000}{215}\] \[215\overset{18}{\overline{\left){\begin{align} & 4000 \\ & \frac{-215}{\begin{align} & 1850 \\ & \frac{-1720}{130} \\ \end{align}} \\ \end{align}}\right.}}\]

Hence, \[18\] shirts can be stitched and \[130\text{ }cm\text{ }\left( 1\text{ }m\text{ }30\text{ }cm \right)\] cloth will be left.


10. Medicine is packed in boxes, each weighing \[\mathbf{4}\text{ }\mathbf{kg}\text{ }\mathbf{500}\text{ }\mathbf{g}\] . How many such boxes can be loaded in a can which cannot carry beyond \[\mathbf{800}\text{ }\mathbf{kg}\]?

Ans:

Weight of a box \[\begin{align} & =\text{ }4\text{ }kg\text{ }500\text{ }g\text{ } \\ & =\text{ }4500\text{ }g \\ \end{align}\]

Number of boxes \[=\text{ }\frac{800000}{4500}\]

\[4500\overset{177}{\overline{\left){\begin{align} & 800000 \\ & \frac{-4500}{\begin{align} & 35000 \\ & \frac{-31500}{\begin{align} & 35000 \\ & \frac{-31500}{3500} \\ \end{align}} \\ \end{align}} \\ \end{align}}\right.}}\]

Hence, \[177\] boxes can be loaded in the Van.


11. The distance between the school and the house of a student’s house is \[\mathbf{1}\text{ }\mathbf{km}\text{ }\mathbf{875}\text{ }\mathbf{m}\]. Every day she walks both ways. Find the total distance covered by her in six days.

Ans:

Distance between school and her house \[=\text{ }1875\text{ }m\]

Total distance covered \[\begin{align} & =\text{ }2\times 1875\text{ } \\ & =\text{ }3750\text{ }m \\ \end{align}\]

Distance covered in \[6\text{ }days\] \[\begin{align} & =\text{ }6\times 3750\text{ } \\ & =\text{ }22500\text{ }m \\ \end{align}\]

Thus, she covers \[22\text{ }km\text{ }500\text{ }m\] distance in \[6\text{ }days\]


12. A vessel has \[\mathbf{4}\text{ }\mathbf{liters}\text{ }\mathbf{and}\text{ }\mathbf{500}\text{ }\mathbf{ml}\] of curd. In how many glasses each of \[\mathbf{25}\text{ }\mathbf{ml}\] capacity, can it be filled?

Ans:

Capacity of vessel\[\begin{align} & =\text{ }4\text{ }liters\text{ }500\text{ }ml\text{ } \\ & =\text{ }4500\text{ }ml \\ \end{align}\]

Capacity of a glass \[=\text{ }25\text{ }ml\]

Number of glasses can be filled \[=\text{ }\frac{4500}{25}\] \[25\overset{180}{\overline{\left){\begin{align} & 4500 \\ & \frac{-25}{\begin{align} & 200 \\ & \frac{-200}{0} \\ \end{align}} \\ \end{align}}\right.}}\]

Therefore, \[180\] glasses are required.


Practice and Master the Concepts of the Chapter Knowing Our Numbers Class 6 Maths Chapter 1

1.1 Introduction

As students entered into the sixth standard, the NCERT solutions try to recall all their knowledge on numbers at the beginning of the chapter. As the students already learned different calculations like Asian, subtraction, multiplication, and division with the numbers, here, they may learn other ways to calculate or count the big numbers to express huge quantities.


1.2 Comparing Numbers

The Class 6 Maths Chapter 1 Solutions PDF contains the topic  “Knowing Our Numbers" to teach the students of grade 6 about comparing the larger numbers in different ways. Students can learn how to change the value of a number by shifting the digits, changing their places. Also, the subject experts explained the introduction of big numbers like 10,000 and 1,00,000. Not only numbers of students also taught how to find out the place value as well as keeping commas for the big numbers.


It ultimately deals with the reading and writing strategies of 5 - digit and 6 - digit numbers. So that the students can calculate more values while finding different problems as well as they are useful in their daily routine also.


  • 1.2.1 How many numbers can you make?

  • 1.2.2 Shifting of numbers.

  • 1.2.3 Introducing 10,000.

  • 1.2.4 Revisiting place value.

  • 1.2.5 Introducing 1,00,000.

  • 1.2.6 Larger numbers.

  • 1.2.7 An aid in reading and writing large numbers.


1.3 Large Numbers in Practice

This part of Chapter 1 is important for Class 6 students to improve their thinking skills in math. It introduces the concept of estimation, teaching students how to estimate future events and plan for them. The chapter provides examples and scenarios to help students understand and practice estimating and forecasting. It also covers rounding numbers and basic arithmetic with large numbers.


  • 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

Introducing the usage of brackets is essential for 6th-grade students. The usage of brackets will occur mostly and two or more different things with one common point.so the students need to place the different things in a bracket, and the common thing will be outside the bracket. Students also learn the distribution of common things, which is outside the bracket to the different parts available within the brackets.


1.5 Roman Numerals

As the students knew the Hindu Arabic numeral system till primary classes, here they are introduced to the Roman numeric system, which is widely spread in the society. So, it is mandatory to teach them with several examples and perfect explanations. It can be easily done by NCERT Solutions Class 6 Maths Chapter 1.


Overview of Deleted Syllabus for CBSE Class 6 Maths Chapter 1 Knowing Our Numbers 2024-25

Dropped Topics Name

Estimating to the nearest tens by rounding off - 1.3.1 &1.3.2

Estimating to the nearest hundreds by rounding off - 1.3.3 

Estimating to the nearest thousands by rounding off - 1.3.4

Estimating outcomes of number situations - 1.3.5 

To estimate sum or difference - 1.3.6 

To estimate products - 1.3.7 

Using brackets - 1.4

Expanding brackets - 1.4.1

Roman numerals - 1.5


Exercises of Class 6 Maths Chapter 1 Knowing Our Numbers

Exercise

Number of Questions

Exercise 1.1

4 Questions & Solutions

Exercise 1.2

12 Questions & Solutions

Exercise 1.3

5 Questions & Solutions

Exercise 1.4

9 Questions & Solutions

Exercise 1.5

2 Questions & Solutions

Exercise 1.6

5 Questions & Solutions

Conclusion

The NCERT solutions for "Knowing Our Numbers" will help you understand place value, which is how the position of digits affects the value of a number. You will also learn how to compare and rank numbers, understand greater than, less than, and in-between figures, and work with larger numbers like thousands and crores. Additionally, you will learn how to write numbers using brackets and Roman numerals. In previous year question paper there were around 8-10 questions asked from the given topic.


Other Study Material for CBSE Class 6 Maths Chapter 1


Chapter wise NCERT Solutions for Class 6 Maths

Given below are the chapter-wise NCERT Solutions for Class 6 Maths. Go through these chapter-wise solutions to be thoroughly familiar with the concepts.


FAQs on NCERT Solutions for Class 6 Maths Chapter 1 - Knowing Our Numbers

1. What Makes NCERT Solutions the Best Choice?

Of course, the NCERT solutions are a perfect choice for the students with their distinct features. They are concerned more about the level of the students, and the subject experts will prepare the material in such a way which is easy to understand and good to practice.


The availability of PDF for free download is another positive feature that makes it more weight. Session of doubts clarification was fabulous for the students to get the clarification as well as confidence while solving problems.

2. 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?

Cloth needed to stitch a single shirt  = 2m 15cm

= 200 cms + 15 cms

= 215 cm

Total cloth = 40 m

                 = 4000 cms

Number of shirts can be stitched with 4000 cm = 4000/ 215 cms

      = 215*18 = 3870

      = 18 shirts.

Remaining cloth = 4000 - 3870 = 130 cms.

So 18 shirts can be stitched with 40 m of cloth with 130 cm cloth will remain.

3. What are the topics covered in Chapter 1 of NCERT Solutions for Class 6 Maths?

The topics covered in the NCERT Solutions for Chapter 1 of NCERT Class 6 Maths are:

  • Comparing numbers- reading and writing 5 and 6 digit numbers

  • Estimation of figures

  • Usage of brackets

  • Roman numerals

This chapter is important as students will use the basics learnt here in various life situations too. Therefore students should make it a point to clear the fundamentals of this chapter.

4. How many problems are there in each exercise of NCERT Solutions for Chapter 1 of Class 6 Maths?

There are three exercises in NCERT Solutions for  Chapter 1 of Class 6 Maths-

  • Exercise1.1- four questions with answers

  • Exercise 1.2- 12 questions with answers

  • Exercise 1.3- three questions with answers

Students can find the NCERT solutions to all exercises free of cost on Vedantu’s website. Solving all these exercise questions will make the fundamentals of students clear and will help them score well in exams.

5. Why should I refer to NCERT solutions for Chapter 1 of Class 6 Maths?

NCERT solutions for Class 6 Maths Chapter 1 builds from the fundamentals so that students can grasp the basics and progress to advanced concepts easily. You can refer to Vedantu’s NCERT solutions for free of cost to get an in-depth understanding of Chapter 1 Class 6 Maths. These solutions are prepared by experts who have decades of teaching experience and are written in easy to understand language.

6. How can I learn Maths in Chapter 1 of Class 6 Maths?

Students can learn Class 6 Maths from the NCERT textbook. The concepts are explained easily and taught from the basics so that all students can understand them. There are exercise questions at the end of each chapter that will test the student’s understanding of the concepts. Students can practice those questions to better understand the topic. Vedantu app and the website offers solutions to all exercise questions so that students can solve their doubts and learn how to solve each problem.

7. What are the rules of the Roman numeral system?

The rules followed while writing numbers in Roman numerals are-

  • The value of a symbol is added as many times as it repeats.

  • A symbol is never repeated more than three times except for V, Land D where it is never repeated.

  • The lower value symbol is added when it is present on the right side of a higher value symbol.

  • The lower value symbol is subtracted when it is present on the left side of a higher value symbol.

  • V, L and D are never subtracted.

8. What is the topic of class 6th maths chapter 1?

NCERT Solutions for Class 6 Maths, Chapter 1, covers the following topics:

  1. An overview of numbers

  2. Comparing figures

  3. Both descending and ascending order

  4. With a given set of digits, how many numbers can be formed?

  5. Modifying the numbers

  6. Set the value

  7. Greater figures and approximations

  8. Calculating the total or difference

  9. Calculating numerical products

  10. BODMAS

  11. Making use of brackets

9. How do you introduce whole numbers in Class 6?

You already have a solid foundation in maths from prior years in Class 6. To expand on that understanding, introduce whole numbers in the following way:

  1. Establish a connection with well-known ideas: Remind kids to count the numbers (1, 2, 3,...) that they encounter on a daily basis.

  2. Present Zero: Talk about the significance of the placeholder zero and the idea of "nothing."

  3. Emphasise Location Significance: Use manipulatives to show how a digit's value varies according to its position (ones, tens, hundreds, etc.), such as place value blocks or number charts.

  4. Examine Similarities: Practice utilising the more than (), less than (>), and equal to (=) signs while comparing numbers using real-world examples (apples, marbles).

  5. Explain How to Place Orders: Use number lines or activities such as lining up pupils from smallest to tallest to arrange numbers in ascending (increasing) and descending (decreasing) order.

10. How many types of numbers are there in Ncert Class 6 Maths Chapter 1?

  • Natural Numbers: These are the numbers that may be counted infinitely, beginning at 1. 1, 2, 3, 4,...

  • Whole Numbers: These consist of zero and every natural number, including 0, 1, 2, 3, 4,...

  • All whole numbers, as well as their negatives and zero, are considered integers. ..., 0, 1, 2, 3, -2, -1, -3,...

  • Fractions: A fraction bar separates the numerator and denominator, which symbolise the portions of a whole that a fraction represents: ½, ¾,...

  • Decimals: Numbers lower than one or fractions of a whole represented by a decimal point are called decimals. 0.5, 0.75,...

  • Rational numbers: are those that may be written as fractions in which the denominator is not zero and the numerator and denominator are both integers: ½, -3/4, 0.25, etc.

  • Irrational Numbers: Irrational numbers are those that have an infinite decimal representation that never repeats and cannot be stated as a fraction of two integers: Pi is π, the square root of two is √2,...

11. What are the natural numbers in Class 6 Math Chapter 1?

Natural numbers, which begin at 1 and go on indefinitely (1, 2, 3, 4, 5,...), are essentially the positive counting numbers. These are the numbers, which exclude zero (0), that you use to count items.

12. What is the unique number class 6?

There's no specific thing called a "unique number." But students learn about different kinds of numbers: natural numbers, whole numbers, integers, fractions, decimals, rational numbers, and irrational numbers. Each type of number has its own special properties.


For example, natural numbers are for counting things, while fractions show parts of a whole. Understanding each type of number helps students solve math problems and see how numbers are used in the real world.

13. How many problems are there in each exercise of NCERT Solutions for Class 6 Maths Chapter 1?

Students who regularly practise the exercise-based issues will have a better understanding of the subjects covered. Each of the exercises in Chapter 1 has the following amount of questions:

  • Exercise 1.1 – 4 questions

  • Exercise 1.2 – 12 questions

  • Exercise 1.3 – 3 questions