Question

Find the difference between the place value and face value of the digit $ 6 $ in the number $ 72601 $ .

Answer 1

Hint: In order to find the difference between the place value and face value of the number $ 6 $ , we need to know the details about the face value and place value of a number. As the name defines, the face value shows the value of the number and for the place value it shows the place of the number, at which place or position the number is located.

Complete step-by-step answer:
So, we are given a number $ 72601 $ .
We need to find the difference between the place value and the face value of the digit $ 6 $ from the number $ 72601 $ , for that first we need to know about the face and place value.
From the basic definitions, we know that the face value of a number shows the value of the digit itself, whereas the place value describes the position of the digit of the number, at which position the value is located.
So, from the definitions the face value is the digit itself.
Therefore, the face value of digit $ 6 $ in the number $ 72601 $ is - $ 6 $ . ……(1)
Now, for the place value counting the number of digits after digit $ 6 $ from left to right in the number given, we can see there are $ 2 $ digits on the right side, so multiplying the face value with $ 10 $ raises to the power the number of digits on the right side.
Therefore, the place value becomes: $ {\text{Face value}} \times {\text{1}}{{\text{0}}^2} $
Substituting the face value, we get:
Place value \[{\text{ = 6}} \times {\text{1}}{{\text{0}}^2} = 6 \times {\text{100 = 600}}\] (2)
For the difference, subtracting the face value (equation 1) from the place value (equation 2):
Difference $ = 600 - 6 = 594 $ .
Hence, the difference between the place value and face value of the digit $ 6 $ in the number $ 72601 $ is $ 594 $ .
So, the correct answer is “ $ 594 $ ”.

Note: Remember, face value always remains the same, but the place value changes with place or position.
We can use a simple formula to calculate the place value for any number, that is: $ {\text{Face value}} \times {\text{1}}{{\text{0}}^x} $ , where $ x $ is the counting of digits after the face value from left to right.