Place Value & Face Value – Differences and Applications

What is the meaning of Place Value?

Place value  or Local value is simply the value of the digit as per its position in the number. It is extremely easy to calculate the place value of a number. For example, as shown below, in the number 561- the digit 5 is at the hundreds place, 6 is at the tens place and 1 is at the ones place. Hundreds, tens and ones represent the digit value. The numbers 5,6 and 1 represent the numerical value. We get the place value by multiplying the numerical value with the digit value. Here, the place value of 6 will be 6 x 10 = 60 (numerical value x digit value = place value)

Quick questions:

1. What is the place value of 4 in the number 524? Ans. 4 x 1 = 4
2. What is the place value of 7 in the number 783? Ans.7 x 100 = 700
3. What is the place value of 2 in the number 2106? Ans. 2 x 1000 = 2000
4. What is the place value of 0 in the number 30,956? Ans. 0 x 1000 = 0

What is the meaning of Face Value?

Face value just describes the value of the digit itself. More simply, it is the digit itself. For Example, in the table below, the face value of 5 will be 5. Similarly, the face value of 6 will be 6 and 1 will be 1 irrespective of where the digit is placed in the number.

1. What is the face value of 4 in the number 524? Ans.  4
2. What is the face value of 7 in the number 783? Ans. 7
3. What is the face value of 2 in the number 2106? Ans. 2
4. What is the face value of 0 in the number 30,956? Ans. 0 

Difference between Place Value and Face Value

The only similarity between place value and face value is the value of number 0. It is always 0 irrespective of where it is placed. The place value and face value remain the same for the digit at the ones place. 

Understanding Place Value and Face value through Expanded form

The expanded form of a number can be written as:

In the expanded form, the number is expressed through the sum of the place value of the digits. 

Here, place value of 8 is 800 (since 8 is at the hundreds place), 5 is 50 ( 5 is at the tens place) and 2 is 2 (2 is at the ones place) so the number can be expressed as the sum of the place values of the digits. However, the face value still remains the same number itself.

Place Value and Face Value according to the Indian and International number system

The place value of a number is written in the same manner but are read differently depending on the number system they are used in. For example, the number is 546810923. The place value is read as given in the chart below:

The place value of 8 here is written as 8 x 1,00,000 = 8,00,000. It is read as 8 Lakhs. Now, observe the International place value system in the chart below:

The place value of 8 here is written as 8 x 1,00,000 = 8,00,000. However, it is read as 8 Hundred Thousand. 

When it comes to the Face Value of a digit, it always remains the number itself across different number systems. So the face value of 8 is 8 in both Indian and International Place Value System.

Understanding Decimal Place Values and Face Values

Unlike whole numbers, the decimal place values are different. Decimal numbers consist of whole numbers to the left of the decimal and the fractional part on the right of the decimal. A decimal number can be written in the following expanded form:

Now the place value of the digit just after the decimal is tenth, followed by hundredth thousandth etc.

1. What is the place value of 7 in 54.257? Ans Thousandth (0.007)
2. What is the place value of 2 in 631.28? Ans Tenth (0.2)
3. What is the place value of 9 in 54.098? Ans Hundredth (0.09)
4.  What is the place value of 1 in 12.546? Ans Hundreds (1×10 = 10)