What is the meaning of value in math

The main difference between place value and face value is that 'place value' gives the value of a digit based on its position in a number, whereas, 'face value' is the actual value of a digit in a number. The face value of a number is definite and cannot be changed, whereas, the place value of a number changes according to the digit's place.

Definition of Place Value and Face Value

Place Value

Place value is defined as the value of each digit in a number. We get the place value of a number by multiplying the digit value with its numerical value. Let us understand this with the help of an example.

Example: Find the place value of all the digits in the number 3279.

Solution: In the number 3279, to get the place value of the numbers, we need to multiply each number by the digit value.

• The place value of 3 can be calculated by multiplying 3 (numerical value) by 1000 (digit value), that is, 3 × 1000 = 3000, since 3 is in the thousands place. Similarly, we can find the place values of the rest of the digits in the number.
• The place value of 2 can be calculated by multiplying 2 by 100, that is, 2 × 100 = 200 because 2 is in the hundreds place.
• The place value of 7 can be calculated by multiplying 7 by 10, that is, 7 × 10 = 70 because 7 is in the tens place.
• The place value of 9 can be calculated by multiplying 9 by 1, that is, 9 × 1 = 9 because 9 is in ones place.

Face Value

The face value of a digit in a number is the same digit itself. Let us understand this with the help of an example.

Example: Find the face value of all the digits in the number 3279.

Solution: The face value of every digit is the number itself.

• The face value of '3' is 3 itself.
• The face value of '2' is 2 itself.
• The face value of '7' is 7 itself.
• The face value of '9' is 9 itself.

Observe the figure given below to understand the difference between the place value and face value of the number 3279.

Expanded Form

Let us understand the difference between place value and face value through the expanded form of a number. The expanded form of 432 = 400 + 30 + 2. In the expanded form, we express a number as the sum of the individual digit's place value. In the number 432, the place value of 4 is 400 (since 4 is in hundreds place), the place value of 3 is 30 (since 3 is in tens place), and the place value of 2 is 2 (since 2 is in ones place). However, in the same number 432, the face value of 4 is 4, the face value of 3 is 3, and the face value of 2 is 2.

Difference Between Place Value and Face Value

The table shown below lists the major differences between the place value and the face value of a number.

☛ Related Articles

• Number Systems
• Place Value
• Expanded Form
• Place Value Calculator
• Indian Place Value Chart
• International Place Value Chart
• Decimal Place Value

FAQs on Place Value and Face Value

What is the Difference Between Place Value and Face Value?

Place value is defined as the position that a digit occupies in a number, whereas, face value is the actual value of a digit in a number. For example, in 4538, the place value of 5 is 500 and the face value of 5 is 5 itself.

How to Find the Face Value of a Digit?

The face value of a digit in a number is the digit itself. For example, in 342, the face value of 3 is 3, the face value of 4 is 4, and the face value of 2 is 2.

How to Find the Place Value of a Digit?

To get the place value of a number, we multiply the digit value with its numerical value. For example, in the number 512, to get the place value of '5' we multiply 5 (numerical value) by 100 (digit value) and get 500, since 5 is in hundreds place.

What is the Place Value of 5 in 8756?

In the number 8756, the place value of 5 is 50. Since 5 is in tens place, we multiply 5 by 10 which is equal to 50.

What is the Place Value and Face Value of 0 in a Given Number?

The place value of 0 in any given number is always zero. This is due to the reason that to get the place value of a number, we multiply the digit value with its numerical value, and 0 multiplied by any number is zero. For example, in 4037, the place value of 0 can be calculated by multiplying 0 by 100 because 0 is in the hundreds place. This means 0 × 100 = 0. Therefore, the place value 0 is 0 in any number. Similarly, the face value of 0 is 0 because the face value of a number is the number itself.

What is the Difference Between Place Value and Face Value of 4 in 3412?

The place value of 4 in 3412 is 400 and the face value of 4 in 3412 is 4. The difference between the place value and face value of 4 in 3412 is 400 - 4 = 396.

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