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Difference Between Place Value and Face Value

Difference Between Place Value and Face Value

The place value and the face value of any number are always evaluated with respect to a certain number. A number only makes sense in mathematics if that number is numerically definable.

The value of a number can be said to be a combination of place value and face value. The place value is dependent on position, and its magnitude increases from right to left while the face value of any number is a universally defined constant, and no change in its magnitude is possible. Together, place value and face value help us in determining the overall value of a given number.

Face Value

The face value of any number is defined as the magnitude the number possesses naturally, irrespective of its position in a number. For example, in the below-given number: 3526 The face value of digit 2 is 2. This is the universally defined value of digit 2. Therefore, it remains constant under any circumstance, and no change can be considered in its face value.

Place Value

Its position decides the place value of a digit in a number. The magnitude of the place value increases as we move from right to left. This means that the digit lying on the extreme left of any number has the highest place value in that number. The value of each position in a number can be given in increasing order as one, ten, hundred, thousand, ten thousand, etc. Thus, to find the place value of any digit, we only have to multiply the face value of that digit with the value of its position.

This is illustrated below: To find the place value of the digit 6 in the number 4683, we will first consider the face value of that digit, which is 6. Then we multiply it with the value of position where the digit is. For example, the value of position occupied by the digit 6 is 100. Therefore, by multiplication, we get the place value of 6 in the number 4683 as 600. The place value of any digit changes with the change in its position.

Using the above-described method, we can also write a number in expanded form by considering it as a sum of all the place values of that number. For example, the number 4683 can be written in the expanded form as: 4000 + 600+ 80+ 3 This notation helps visualise the actual magnitude of any number.

Difference

 

Place Value

Face Value

- The place value of any digit is defined as the product of the face value of that digit with the value of its position.

- The place value of any digit changes with the position of that digit.

- The value of positions in a number increases by a factor of 10 as we move from right to left.

- We can write a number in expanded form as a sum of all the place values of its digits.

- Face value is defined as the natural magnitude of any digit that is universally defined.

- The face value remains constant irrespective of its position within a number.

- The face value of any number is always in single digits.

- Face value is used in the calculation of the place value of any digit.

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