Question

Place value and face value are always equal at which place?
(a) Hundreds
(b) Ones
(c) Thousands
(d) Tens

Answer 1

Hint: We solve this problem by using the definitions of face value and place value of a number.
The place value is defined as the digit multiplied wherever it is placed, either at hundreds or thousands.
Face value is defined as the digit itself.
We take the example of a 4 digit number and find where the face value and place value are equal.

Complete step by step answer:
We are asked to find where the place value and face value are equal
Let us take an example of 4 digit number as 1234
Now, let us find the place value and face value for each and every digit of the number 1234.
(1) For the digit 4
We know that face value is defined as the digit itself.
By using the above definition we get the face value as
\[\Rightarrow F=4\]
We know that place value is defined as the digit multiplied wherever it is placed, either at hundreds or thousands.
By using the above definition we get the place value as
\[\begin{align}
  & \Rightarrow P=4\times 1 \\
 & \Rightarrow P=4 \\
\end{align}\]
(2) For digit 3
By using the face value definition we get the face value as
\[\Rightarrow F=3\]
Similarly, by using the place value definition we get the place value as
\[\begin{align}
  & \Rightarrow P=3\times 10 \\
 & \Rightarrow P=30 \\
\end{align}\]
(3) For digit 2
By using the face value definition we get the face value as
\[\Rightarrow F=2\]
Similarly, by using the place value definition we get the place value as
\[\begin{align}
  & \Rightarrow P=2\times 100 \\
 & \Rightarrow P=200 \\
\end{align}\]
(4) For digit 1
By using the face value definition we get the face value as
\[\Rightarrow F=1\]
Similarly, by using the place value definition we get the place value as
\[\begin{align}
  & \Rightarrow P=1\times 1000 \\
 & \Rightarrow P=1000 \\
\end{align}\]
Here, we can see that in all cases the face value and place value are equal only at one place.
Therefore, we can conclude that place value and face value are equal at one’s place.
So, option (b) is the correct answer.

Note:
We can explain the above result in a direct method.
By using the definitions of face value and place value we can say that both are equal when the place value is multiplied by 1
This is because the face value is the digit itself while for place value we need to multiply the digit with its place. These two are equal if and only if the multiplied number is 1
Therefore, we can conclude that place value and face value are equal at one’s place.
So, option (b) is the correct answer.