# 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)

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 = 30007 is 7 × 100 = 7002 is 2 × 10 = 20 0 is 0 × 1 = 0 3 being at Th-place7 being at H-place2 being at T-place0 being at one’s or unit’s place

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

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

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