# 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
 1 0 0 0 0 0 0 0 0 0 0 0 100000 10000 1000 100 10 1 Decimal point 0.1 0.01 0.001 0.0001 0.00001 0.000001 2 4 3 1 8 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 value 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.

### Practice Questions

1. Which of the following shows the correct place of $5$ in $12, 450$?

2. Which of the following shows the correct place of $8$ in $10, 800$?

3. Which of the following shows the correct place of $7$ in $5.7098$?

4. Which of the following shows the correct place of $8$ in $54.10812$?

5. Which of the following shows the correct place value of $7$ in $12, 078$?

6. Which of the following shows the correct place value of $5$ in $105, 608$?

7. Which of the following shows the correct place value of $6$ in $104.056$?

8. Which of the following shows the correct place value of $4$ in $12.0459$?

9. True or False: The place value of the leftmost $8$ is ten times larger than the rightmost $8$ in $28, 781$.

10. True or False: The place value of the leftmost $6$ is a thousand times larger than the rightmost $6$ in $461, 964$.