NCERT Workbook Solutions For Class 3 Chapter 1 Numbers

NCERT Workbook Solutions For Class 3  Chapter 1 Numbers Introduction

The number is an idea which has different meanings according to the way we use them.

• The number is made up of digits and has different values or numerals.
• The number system helps us to group numbers according to their properties.
• Place value and face value of numbers help us to define the numbers and arrange them in ascending or descending order.
• Understanding the value of a number helps in comparing numbers.

Vishal was a new student in the class. The class teacher asked him to introduce himself.

You can see that like Vishal, we use so many numbers in our daily life, which have different meanings years refers to the age of Vishal and 37 refers to the door number of his house. Let us get to know about numbers.

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NCERT Workbook Solutions For Class 3  Chapter 1 Number System

Digits are single units that form the numeral. They are 0, 1, 2, 3, 4, 5, 6,7, 8, 9.

DecimaI number system or the Hindu-Arabic number system, the numbers are symbols or digits from zero to nine (0, 1, 2, 3, 4,5,6,7,8,9).

A system is the grouping of similar things based on a few rules. Let us see how numbers are grouped in a system.

• Natural Number System: All countable numbers from one to infinity are called Natural numbers. Natural numbers are denoted by the symbol ‘N’.
• Counting (Natural) Numbers: 1,2,3, 4,5…
• Whole Number System: The teacher asked a very interesting question to Vishal. “Vishal, can you tell me how old you were, on the day you were born?” What do you think will be Vishal’s answer? “Zero”! Zero is a very interesting number. lt can mean nothing or it can mean a very large value depending on where it is written.
• Zero, together with natural numbers forms the Whole number System.
• Whole Numbers: 0, 1, 2, 3, 4, 5…
• Place value of numbers: Place value gives the value of a numeral based on its position in a number. Their values are determined from right to left as ones, tens, hundreds, thousands, ten thousand, etc.

Vishal has collected 157 stamps. Let’s find the value of this numeral.

157 = 100 + 50 + 7 (One hundred, five tens and seven ones)

Place value of numbers Example:

2574 = 2000 + 500 + 70 + 4 (Two thousand five hundred and seventy-four)

55023 = 50000 + 5000 + 0 + 20 + 3(Fifty-five thousand and twenty-three)

Face value of numbers: The value of a digit in a number is called its face value. The face value of a number remains the same irrespective of its position.

Face value of numbers Example:

1. The face value of 7 in 157 is seven and its place value is seven ones.
2. The face value of 7 in 2574 is seven and its place value is seventy.

NCERT Workbook Solutions For Class 3  Chapter 1 Number System

Question 1. Choose the correct alternative.

1. How many 10 do you need to make 1000?

1. 100
2. 50
3. 20
4. 10

Answer:

2. The expanded form of 705 is

1. 70+5
2. 7+5
3. 700+5
4. 7+0+5

Answer:

3. The number just after 100 is

1. 101
2. 99
3. 110
4. 111

Answer:

4. The smallest two-digit number is

1. 11
2. 22
3. 10
4. 99

Answer:

5. The number, one less than 66 is

1. 61
2. 65
3. 67
4. 55

Answer:

Question 2. Match the Column-1 with Column-2.

1. (1) (C), (2) (D), (3) (A), (4) (B)
2. (1) (A), (2) (D), (3) (C), (4) (B)
3. (1) (B), (2) (A), (3) (D), (4) (C)
4. (1) (C), (2) (D), (3) (B), (4) (A)

Answer:

Question 3. State whether the following statements are true or false.

1. The face value of 8 in 489 is 8. ()

2. The place value of ‘t’ in 415 is one ()

Answer:

Question 4. Fill in the blanks.

1. 100, 102, __, 106, __,110.
Answer:

2. 5507=5000+ __ +7.
Answer:

Question 5. Very Short Answer Type Questions.

Find out the value of numbers, place values, and face values of the following:

1. 4 in three thousand four hundred and fifty-six.

Number:

Place Value:

Face value:

Answer:

2. 6 in five thousand and sixtY-two.

Number:

Place value:

Face value:

Answer:

Question 6. Short Answer Type Questions.

1. How many hundreds are there in 8000? What is the face value and place value of 8 in 8000?
Answer:

2. Write the expanded form of 40732. How many thousands are there in this number?
Answer:

NCERT Workbook Solutions For Class 3  Chapter 1 Numbers Activity Corner

Identify the number.

Expanded form: ______

Standard form: ______

Place value of 1: ______

NCERT Workbook Solutions For Class 3  Chapter 1 Numbers Ordering Numbers

Ascending order is arranging numbers from the smallest to the greatest value.

• Descending order is arranging numbers from greatest to the smallest value
• Learn to write numbers in ascending and descending order.

Look at these two sets of Chennapatna organic wooden toys. The dolls in picture A can be stacked one inside the other when you arrange them from smaller size to bigger size.

ln picture B, the wooden rings are arranged from bigger to smaller to create a beautiful toy. Have you seen these toys?

Ascending order: Arrange the numbers from smaller values to greater values.

Ascending order Example:

1. 400,25, 1,60, 45,5003.

Ascending order: 25<45<L60< 400< 5003.

2. 4005, 2003,3004,1001.

Ascending order: 1001 < 2003 < 3004 < 4005.

Descending order: Arranging the numbers from greater value to the smaller value.

Descending order Example:

1. 8481,8850, 8586, 8611, 8516.

Descending order: 8850 > 8611 > 8586 > 8516 > 8481.

(These are the heights of the five tallest mountains of the world (in metres), with the tallest being Mount Everest at the height of 8850 meters.)

2. 5432, 2922, 2656, 7749.

Descending order: 7749 > 5432> 2922> 2656.

Predecessor and Successor:

We can find the predecessor and successor of every number in the whole number system.

Predecessor of a number is a number which comes just before it or a number which is one less than the number.

Predecessor of a number Example:

Predecessor of 9 = 8 (9 – f = a)

Predecessor of 100 = 99 (100 – 1 = 99).

(Observe that ‘zero’ does not have a predecessor.)

Successor of a number is a number which comes just after it or a number which is one more than the number.

Successor of a number Example:

Successor of 500 = 501 (500 + 1 = 501).

Successor of 9999 = 10000 (9999 + l- = 10000).

NCERT Workbook Solutions For Class 3  Chapter 1 Numbers Ordering numbers

Question 1. Choose the correct alternative.

1. The ascending order of 51, 41, 21, 61 is

1. 21 <41<51 <61
2. 61 <51 <41<21
3. 21 > 41 > 51 > 61
4. 41 < 21 < 61 < 51

Answer:

2. The sum of the predecessor and successor of 100 is

1. 102
2. 100
3. 200
4. 300

Answer:

3. The difference between a number and its successor is always

1. 1
2. 2
3. 5
4. 10

Answer:

4. Choose the correct one arranged in descending order.

1. 3<6<9<12
2. 100<200<300<400
3. 99>89>79>69
4. 22<32<42<52

Answer:

5. The difference between 99 and its successor is

1. 5
2. 4
3. 2
4. 1

Answer:

Question 2. Match the Column-1 with Column-2.

1. 1 (D), 2 (E), 3 (A), 4 (B), 5 (C)
2. 1 (C), 2 (E), 3 (A), 4 (B), 5 (D)
3. 1 (C), 2 (B), 3 (E), 4 (A), 5 (D)
4. 1 (C), 2 (A), 3 (E), 4 (B), 5 (D)

Question 3. State whether the following statements are true or false.

1. 1. 2003 is greater than 2030 ()
2. 2. The successor of 972 = 972 + 1 ()

Answer:

Question 4. Fill in the blanks.

1. ___ <355< ___ < 365
Answer:

2. ___ <99< ___ < 9999
Answer:

3. ___ <707 < ___ < 709
Answer:

Question 5. Very Short Answer Type Questions.

1. Number of trees in five different parks in the city – 111, 101,11,110. Arrange in ascending order.

Answer:

2. Number of schools in five districts – 415,455,405,445. Arrange in ascending order.

Question 6. Short Answer Type Questions.

1. The following are the temperatures recorded in different cities. Arrange them in descending order.

36°C, 45°C, 39°C, 44°C, 32°C

Answer:

2. Write the following set of numbers in descending order.

Answer:

Question 7. Activity Corner

1. Identify the missing number.

NCERT Workbook Solutions For Class 3  Chapter 1 Numbers Comparing Numbers

Once we understand the value of numbers, we can write the greatest and smallest number from the given digits and can easily compare two or more digits.

Writing the greatest and smallest number from the given digits

Follow the simple rules :

1. Write the given digits in ascending order.
2. For the greatest number, write the digits from the highest value to the lowest value.
3. For the smallest number write the digits from the lowest value to the highest value. We will start with a digit other than 0 and write the 0 in second place.
4. ln case, there are two equal digits, then write them at consecutive places.

Comparing Numbers Examples:

Question 1. Write the greatest number that can be formed with digits 9, 3.
Answer: Ascending order 3 < 9.

The greatest number that can be formed is 93 (ninety-three).

Question 2. Write the greatest number that can be formed with digits 7, 3, 5.
Answer: Ascending order 3 <5 < 7.

The greatest number that can be formed is 753 (seven hundred and fifty-three).

Question 3. Write the smallest number that can be formed with 8, 4.
Answer: Ascending order 4 < 8.

The smallest number that can be formed is 48 (forty-eight).

Question 4. Write the smallest number that can be formed with 2, 1, 3.
Answer: Ascending order 1<2<3.

The smallest number that can be formed is 123 (one hundred and twenty-three).

Rounding off numbers

Imagine this, you are shopping in a supermarket and have bought two items. You want to do a quick check of the approximate value. This is where your place value comes in real handy. How?

Let the cost of items be, ₹ 97, < ₹ 228.

The best and easiest way to add is by splitting them according to their place values.

₹97 is nearest to 100

₹212 is nearest to 210

The approximate total will be ₹ 310. (Actual value is ₹309)

Rounding off to the nearest 10

Follow the rules:

1. Check the digit in one’s Place.
2. If it is <5, round it off to less than ten.
3. If it is >5, round it off to the higher ten.

Rounding off to the nearest 10 Examples:

1. Round off t2 to the nearest ten. 2<5, it is closer to 10 than twenty. So, 12 is rounded off to 10.
2. Round off 97 to the nearest ten. 7>5, it is closer to L00 than 90. So, 97 is rounded off to 100.

Rounding off to the nearest 100

Follow the rules:

1. Check the digit in tens Place.
2. If it is <50, round it off to lesser hundred.
3. if it is >50, round it off to the higher hundred

Rounding off to the nearest 100 Examples:

1. Round off 212 to nearest hundred. 12<50,2I2iscloserto hundred than 200. So, 2t2is rounded offto 200.
2. Round off 387 to nearest hundred. 87 > 50, 387 is closer to 400 than 300. So, 387 is rounded off to 400.

NCERT Workbook Solutions For Class 3  Chapter 1 Numbers Comparing Numbers

Question 1. Choose the correct alternative.

1. The smallest possible number that can be written with the digits 1,7, 1, is

1. 177
2. 117
3. 171
4. 711

Answer:

2. The largest possible number that can be written with the digits 0, 5, and 5 is

1. 505
2. 55
3. 50
4. 550

Answer:

3. The number of children in 3 sections of class 5 is 32, 36, and 37. The total number of children to the nearest ten is

1. 120
2. 105
3. 90
4. 110

Answer:

4. 68 rounded off to the nearest ten and hundred will be

1. 50, 100
2. 60, 100
3. 70, 100
4. 70,200

Answer:

5. The numbers 144 and 164 rounded off to the nearest hundred will be

1. 100,100
2. 100,200
3. 200, 100
4. 140,160

Answer:

Question 2. Match the Column-1 with Column-2.

1. 1(D), 2(E), 3(A), 4(B), 5(C)
2. 1(C), 2(E), 3(A), 4(B), 5(D)
3. 1(E), 2(D), 3(B), 4(C), 5(A)
4. 1(C), 2(D), 3(B), 4(A), 5(E)

Answer:

Question 3. State whether the following statements are true or false.

1. 3045 is the smallest possible number with the digits 5,3,0,4 ( )
2. 9810 is the largest possible number with the digits 0, 9, 1, 8 ( )

Answer:

Question 4. Fill in the blanks.

1. The smallest five-digit number is ___ and its successor is -.
2. ___ is the largest 3-digit number and its predecessor is -.

Answer:

Question 5. Very Short Answer Type Questions.

1. 1,6,1,8,2

Largest possible number ____

Smallest possible number ____

Answer:

2. 7,3,5,9,0

Largest possible number ____

Smallest possible number ____

Answer:

Question 6. Short Answer Type Questions.

Question 7. Activity Corner

ln a school, each class was asked to collect newspapers for recycling. The contributions from different classes were as follows. Estimate to the nearest ten, how many new papers were collected approximately?