Determining place value, value and face value

CPEA Mathematics

1. About "Place Value and Face Value"
Place Value and Face Value :
In this section, we are going to learn face value and place value of a particular
digit in the given number.
Place value :
Place value of a digit in a number is the digit multiplied by thousand or hundred
or whatever place it is situated.
For example,
In 25486, the place value of 5 is
= 5 ⋅ 1000
= 5000
Here, to get the place value of 5, we multiply 5 by 1000.
Because 5 is at thousands place.
Face value :
Face value of a digit in a number is the digit itself.
More clearly, face value of a digit always remains same irrespective of the
position where it is located.
For example,

2. In 25486, the face value of 5 is 5.
The difference between place value and
face value
The difference between place value and face has been illustrated in the
picture given below.

Place Value
For better understanding, here we are going to discuss about place value in
detail.
When we look at the picture given below, we can clearly understand place
value.

3. To have better understanding of the picture, let us consider an example.
Find the place value of the digit "5" in the number 25486.
Solution :
As per the first branch, the location of "5" in 25486 is thousands place.
As per the second branch, the value of "5" in 25486 is 5000.
Finally, the place value of "5" in 25486 is "5000"
Shortcut to find place value

4. Steps involved in finding place value
Step 1 :
Write the digit for the one you want to find the place value.
(In 2586791, we want to find the place value of "8")
Step 2 :
Count the number of digits which come after the digit for the one you want
to find the value.
(In 2586791, after 8, we have four digits "6791")
Step 3 :
Since there are four digits (6791) after 8, take four zeros after 8.

5. Then we get 80000.This is the place value of 8
Place value and Face value - Practice
Problems
Problem 1 :
Find the face value and place value of the underlined digit in the number
given below.
253869
Solution :
In the number above, 6 is underlined.
The face value of 6 is the same.
So, the face value of 6 is 6.
To get place value, we have to count the number of digits after 6.
There is only one digit after 6.
So, the place value of 6 is 60.
Problem 2 :
Find the face value and place value of the underlined digit in the number
given below.
563472

6. Solution :
In the number above, 2 is underlined.
The face value of 2 is the same.
So, the face value of 2 is 2.
To get place value, we have to count the number of digits after 2.
There is no more digit after 2.
So, the place value of 2 is 2.
Problem 3 :
Find the place value of "K" in the number given below.
Given that K = 2x and x = 3.
K78952
Solution :
From the given information, let us find the value of "K".
K = 2x = 2(3) = 6 ------------> K = 6
So, we have
K78952 ------------> 678952
To get place value of "K", we have to count the number of digits after 6.
There are five digits after 6.

7. Hence, the place value of "K" is 600000.
Problem 4 :
Find the place value of "K" in the number given below. Given that K is the even
prime number.
78K346
Solution :
From the given information, let us find the value of "K".
K = 2
(Because 2 is the only even prime number we have in math)
So, we have
78K346 ------------> 782346
To get place value of "K", we have to count the number of digits after 2.
There are three digits after 2.
Hence, the place value of "K" is 2000.
Problem 5 :
Find the place value of "K" in the number given below. Given that K is a number
which is less than 10 and exactly divisible by both 2 and 3.
32K58
Solution :

8. From the given information, let us find the value of "K".
K = 6
(Because 6 is the only number less than 10 and also exactly divisible by both
2 and 3)
So, we have
32K58 ------------> 32658
To get place value of "K", we have to count the number of digits after 6.
There are two digits after 6.
Hence, the place value of "K" is 200.