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Place Value – Explanation & Examples

What is a Place Value?

In mathematics, every integer in a number has a place value. Therefore, the place value of a number is the value represented by a digit in a number based on its position in the number.

While a place value is the value a digit holds to be at the place in the number, on the other hand, the face value of a digit for any place in the given number is the value of the integer itself.

A place value chart is a diagram that helps us to find and compare the place value of the digits in numbers through millions. The place value of a digit in the place value chart increases by ten times as we shift to the left and decreases by ten times as we shift to the right.

        PLACE VALUE CHART
100 000 000 000

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     24 318 5  


Example 1

Consider a number: 24.3185

  • The digit 2 is in the tens place, and it has a value of 2 × 10 = 20
  • The digit 4 is in the one’s place, and it has the value of 4 × 1 = 4
  • The digit 3 is in the tenths place, and it has a value of 3 × 1/10 = 3/10 = 0.3
  • The digit 1 is in the hundredths place, and it has a value of 1 × 1/100 = 1/100 = 0.01
  • The digit 8 is in the thousandths place, and it has a value of 8 × 1000 = 8/1000 = 0.008
  • The digit 5 is in the ten-thousandths place, and it has a value of 5 × 10000 = 5/10000 = 0.0005

Therefore, the place value of a number is found by multiplying the face value and the value of the number itself

The place value for a one-digit number is equivalent to its face value. For instance, the 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.

The place value of zero in any number is always zero. Zero may hold any place in a number, but its value will remain to be zero.

Example 2

In numbers having zeros such as 105, 350, 42017, 90218, the place value of 0 in each number is 0.

For a two-digit number, the place value tens digit is 10 times the digit, For example, the place value of 5 in number 57 is 5 x 10 = 50, and the place value of the one-digit is 7 x 1 =7.

Similarly, hundreds of digits’ place value in a three-digit number is 100 x the digit’s face value. For example, the place value of 4 in the number 475 is 4 x 100 = 400.
Thus, for a digit’s place value, the digit is multiplied by the place value of 1; it has to be that place. The methods of finding and writing the place value of any digit in a number are illustrated below with different examples.

Example 3

Write down the place of each digit in the number: 768;

  • The place value of 8 = 8 × 1 = 8
  • The place value of 6 = 6 × 10 = 60
  • The place value of 7 is 7 × 100 = 700.

We can summarize that a number holds its place value as the product of the number and place value of one to be at that position.

Example 4

Find the place value of all digits in the number: 4129.

  • The place value of 9 is 9 × 1 = 9
  • The place value of 2 is 2 × 10 = 20
  • The place value of 1 is 1 × 100 = 100
  • The place value of 4 is 4 × 1000 = 4000

Example 5

Write down the place value of the digits in 2965.

  • The digit 2 is at the thousand’s place; therefore, its place is 1000 x 2 = 2000
  • The digit 9 is the hundred’s place, and so, the place value is 9 x 100 = 900
  • The number 6 is at the ten’s place, so, the place value of 6 = 6 x 10 = 60
  • The number 5 occupies the one’s place in the number 2965; therefore, the place value of 5 is 5 x 1 = 5

Example 6

Write down the place of the digits in the following number: 9721.

  • The number 9 is at a thousand’s place in 9721. So, the place value of 9 is 9 x 1000 = 9000.
  • Another number 7 is at hundred’s place in 9721. Therefore, the place of 7 is equal to 7 x 100 = 700.
  • The number 2 is at the ten’s place. So, the place of 2 in the number 9721 is equal to 2 x 10 = 20.
  • The number 1 occupies the place of ones. And for this case, its place value is 1 x 1 =1.

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