Place Value

The place value of a digit in a number is the value it holds to be at the place in the number. We know about the place value and face value of a digit and we will learn about it in details.


Place, Place Value and Face Value: 

A number is formed by grouping the digits together. 

● Each digit has a fixed position called its place. 

● Each digit has a value depending on its place called the place value of the digit. 

● The face value of a digit for any place in the given number is the value of the digit itself 

● Place value of a digit = (face value of the digit) × (value of the place) 

We know that each digit in a number has a place value. The place a digit occupies in a number tells us its place value. So, the product of the digit and the value of the place it occupies gives us the place value. Let us arrange the digits of the number 5, 32,161 in the following place value chart.

Place Value Table

The face value of a digit in a number is the digit itself.

Properties of Place Value:

1. The place value of every one-digit number is the same as and equal to its face value. 

(i) Place value and face value of 1, 2, 3, 4, 5, 6, 7, 8 and 9 are 1, 2, 3, 4, 5, 6, 7, 8 and 9 respectively.

(ii) The place value of zero (0) is always 0. It may hold any place in a number, its value is always 0.

As, in 105, 350, 42017, 90218 the place value of 0 in each number is 0.


2. In a two-digit number, the place value of the ten-place digit is 10 times of the digit.

As, in 58, the place value of 5 is 5 × 10 = 50 and place value of 8 is 8 × 1= 8; the face value of 5 is 5 and of 8 is 8.


3. In the number 475, the digit 5 is at one’s place, digit 7 is at ten’s place and digit 4 is at hundred’s place.

So, place value of 5 = 5, place value of 7 = 7 × 10 = 70, and place value of 4 is 4 × 100 = 400.

Thus, for the place value of a digit, the digit is multiplied by the place value of 1 it has to be that place.


For Example:

In 768;

the place value of 8 = 8 × 1 = 8

the place value of 6 = 6 × 10 = 60 and

the place value of 7 is 7 × 100 = 700.



4. Now it is the general law that the digit possesses its place value as the product of the digit and place value of one to be at that position. 

For Example:

(i) In a number 4129; 

the place value of 9 is 9 × 1 = 9 as 9 is at one’s or unit’s place.

the place value of 2 is 2 × 10 = 20 as 2 is at ten’s place.

the place value of 1 is 1 × 100 = 100 as 1 is at hundred’s place.

the place value of 4 is 4 × 1000 = 4000 as 4 is at thousand’s place.


(ii) In a number 3720, the place value of

3 is 3 × 1000 = 3000

7 is 7 × 100 = 700

2 is 2 × 10 = 20

0 is 0 × 1 = 0

3 being at Th-place

7 being at H-place

2 being at T-place

0 being at one’s or unit’s place


(iii) Place value of the digits 3702 are shown below:

Place Value of the Digits 3702


(iv) Here, we also see that the place value of the digit 0 in a number is always zero, whatever may be its position.

Place Value of the Digit 0


Place-value of a Digit in a Number:

We know that the position of a digit in a number determines its corresponding value in the number. Let us consider the number 64,19,85,062 and write place-value of each digit in the following chart.

Place-value of a Digit in a Number

We read the above number as thirty-four crore, nineteen lakh, seventy-five thousand, fifty-two.

Place-value of a Digit

Solved Examples Place-value of a Digit in a Number:

1. Write the place-value of 5 in the given numbers:

(i) 50,21,38,761

(ii) 82,05,36,401

(iii) 79,46,15,380


Solution:

Let us arrange the digits in the place-value chart

(i) 

Place-value of 5

Place value of 5 in the number is

5 × 10,00,00,000 = 50,00,00,000. It is read as fifty crore.


(ii)

Place-value of 5 in the Given Numbers

Place value of 5 in the number is

5 × 1,00,000 = 5,00,000. It is read as five lakh.


(iii)

Place-value of a Given Number

Place value of 5 in the number is

5 × 1,000 = 5,000. It is read as five thousand.


2. Write the place value of underlined digits in the given blank.

(i) 5,103

(ii) 7,00,496

(iii) 8,15,924

(iv) 2,18,951


Solution:

(i) 5,103

3 being at one’s or unit’s place

The place value of 3 in the number 5,103 is 3.


(ii) 7,00,496

7 being at Lakhs-place

The place value of 7 in the number 7,00,496 is 7,00,000.


(iii) 8,15,924

2 being at Tens-place

The place value of 2 in the number 8,15,924 is 20.


(iv) 2,18,951

2 being at Lakhs-place

The place value of 2 in the number 2,18,951 is 2,00,000.


3. Circle the following.

(i) Digit at lakhs place - 17,45,015

(ii) Digit with face value of 9 - 49,00,781

(iii) Digit at ten crores place - 92,15,55,470

(iv) Digit at ten thousands place - 75,19,778

(v) Digit at tens place - 92,15,55,470


Solution:

(i) 7

(ii) 9

(iii) 9

(iv) 1

(v) 4


4. Find the place value of 9 in the given numbers.

(i) 6,96,242

(ii) 3,29,162

(iii) 4,52,921

We first arrange the digits of the given number in the place value chart.

Place Value Table Chart

(i) Place value of 9 in the number 6,96,242 is

                   9 × 10,000 = 90,000

 

(ii) Place value of 9 in the number 3,29,162 is

                   9 × 1,000 = 9,000

 

(iii) Place value of 9 in the number 4,52,921 is

                   9 × 100 = 900


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