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158 LearnersLast updated on 16 September 2025
Difference Between Place Value And Face Value
The difference between place value and face value is, face value is the numerical value of the digit, whereas the place value is based on the digit's position in a number (ones, tens, hundreds, etc).
What is Place Value?
The value of a digit depends on its position within the number. Place value is obtained by multiplying the digit by the value of its position.
Example:
|
For 5 in 6532 |
The place value of 5 is 500 because the 5 is in the hundreds place |
|
For 3 in 3641 |
The place value of 3 is 3000 because the 3 is in the thousands place |
What is Face Value?
Face value refers to the actual value of the digit, independent of its position.
Example:
|
For 5 in 6532 |
The face value of 5 is 5 |
|
For 3 in 3641 |
The face value of 3 is 3 |
Difference between place value and face value
| Place Value | Face Value |
| The value is based on its position | The value is the digit itself |
| Changing the position changes its value | Changing the position doesn't change its value |
| In 485, the place value of 4 is 400 because it is at the hundreds position | In 485, the face value of 4 is 4. |
| The rightmost digit's value is its number; moving left, each digit's value increases by a power of ten. | This doesn't depend on the position of the number. |
How to calculate the place value of a digit?
The place value of a digit is calculated by multiplying its face value by its positional value.
Formula: Place value = Face value × Positional Value
Example:
What is the place value of the digits 4, 7, and 8 in the number 24783?
We determine the place value of the digits in 24783 from right to left.
Therefore, the place value of 4, 7, and 8 will be:
4 at the 1000s place, so 4 × 1000 = 4000
7 at the 100s place, so 7 × 100 = 700
8 at 10s place, so 8 × 10 = 80
So, the place value of 4 is 4000, the place value of 7 is 700, and the place value of 8 is 80.
Comparison of Two Numbers with Place Values
Place value helps us identify which number is greater and which is smaller. The place value of a number is determined from right to left. Using place value, we can arrange numbers in order.
1. Numbers with an unequal number of digits.
If one number has more digits than the other, then the number with more digits is always the larger one. For example, between 40 and 400, 40 has 2 digits and 400 has 3 digits. Hence, 400 is the larger number.
2. Numbers with an equal number of digits.
Two numbers with an equal number of digits are compared using the leftmost digit's place value. If the leftmost digit of one number has a greater place value than that of another, then that number is greater.
For example, between 321 and 638
638 is greater
Because the leftmost digit of 321 is 3.
Multiplying 3 by its place value, we get 3 × 100 = 300
Next, the leftmost digit of 638 is 6.
Multiplying 6 by its place value, we get 6 × 100 = 600
When 300 and 600 are compared, the greater number is 600.
Real Life Applications of Place Value and Face Value
The place value and face value are the two basic concepts in mathematics. In our daily life, these concepts are applied in various scenarios like:
- In financial transactions, a $2 note has a face value of 2, but if 2 appears in the tens place, its place value is 20.
- When measuring electricity and water usage, digital meters help determine the value of digits based on their position.
- In time and clocks, while reading digital time like 11:23, the 2 has a face value of 2, but its place value is 20 minutes.
- In computers and data storage, place value is used in binary and decimal systems. The position of each digit decides its value, which is important in tech and data science.
- In population counting and census, place value helps ensure digits in large numbers aren't misplaced. This leads to accurate estimates for planning the national infrastructure of the country.
Common Mistakes and How to Avoid Them in Place Value and Face Value
Dealing with place value and face value can be confusing for kids. It is important to learn their differences correctly. Given below are some mistakes that can be made by students and the solutions that can be applied:
Mistake 1
Incorrectly assigning place values from left to right.
Place values are assigned from right to left.
For example, the correct way to assign place values for the number 3894 is 4 in the ones place, 9 in the tens place, 8 in the hundreds place, and 3 in the thousands place. If the place values are assigned from left to right, it is incorrect.
Mistake 2
Assuming the same digits have the same place value.
When a digit is repeated in a number, children might forget to give it the same place value.
For example, take the number 343. Children might incorrectly assign the same place value to both 3s in the number. The correct place values for the digits in the number 343 are 3 in the ones place, 4 in the tens place, and 3 in the hundreds place.
Mistake 3
Representing smaller numbers with additional place values
Students might give extra place values after the last digit.
For example, in number 52, a child can write 520. Here, ‘0’ as the last digit is unnecessary and gives the wrong result, while writing in words as well.
Mistake 4
Not assigning the place values correctly
Ensure that you assign place values correctly. Children might place the digits incorrectly while expanding them.
For example, 358 will be expanded as 300 + 8 + 50 instead of 300 + 50 + 8. Here, 3 is in the hundreds place, 5 is in the tens place, and 8 is in the ones place.
Mistake 5
Assuming that the face value and place value are the same.
Remember that face value is the digit itself, and place value tells the position of the digit.
For example, find the face value and place value of 7 in 4785. The face value of 7 is 7, and the place value is 700, as it is in the hundreds place.
Solved Examples for Place Value and Face Value
Problem 1
What is the place value of each digit 9, 4, and 8 in the number 46389?
4 = 40000
8 = 80
9 = 9
Explanation
In the number, 46389,
The position of the digit 4 is in the ten thousand place, 6 is in thousands, 3 is in hundreds place, 8 is in tens place, and 9 is in one place.
The place values of the digits 4, 9, and 8 are:
4 × 10000 = 40000
8 × 10 = 80
9 × 1 = 9
So, the place value of 4 is 40000, the place value of 8 is 80, and the place value of 9 is 9.
Problem 2
What is the place value of the 6 in the number 2647?
600
Explanation
In number 2647,
Position of the digit 6 is in 100s
6 is at the 100s place, so 6 ×100 = 600
So, the place value of 6 is 600
Problem 3
What is the place value of the digit 0 in the number 24098?
0 = 100s
Explanation
From left to right in number, 24098
The position of the digit 0 is in 100s, even though 0 does not hold any value.
Problem 4
What is the place value of each digit 7, 5, and 8 in the number 765489?
4 = 4000
7 = 700
8 = 80
Explanation
From left to right in number, 765489
7 is at the 100000s place, so 7 × 100000 = 700000
5 is at the 1000s place, so 5 × 1000 = 5000
8 is at 10s place, so 8 × 10 = 80
So, the place value of 4 is 4000, the place value of 7 is 700, and the place value of 8 is 80.
FAQs on Difference Between Place Value And Face Value
1.What is the face value of 7 in 3456784?
2.What is the place value of 3 in 23789?
3.How to calculate the place value?
4.Write the number 2899 in expanded form using the place value
5.Is it possible for all numbers to have both face value and place value?
6.How can children in Australia use numbers in everyday life to understand Difference Between Place Value And Face Value ?
7.What are some fun ways kids in Australia can practice Difference Between Place Value And Face Value with numbers?
8.What role do numbers and Difference Between Place Value And Face Value play in helping children in Australia develop problem-solving skills?
9.How can families in Australia create number-rich environments to improve Difference Between Place Value And Face Value skills?
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Hiralee Lalitkumar Makwana
About the Author
Hiralee Lalitkumar Makwana has almost two years of teaching experience. She is a number ninja as she loves numbers. Her interest in numbers can be seen in the way she cracks math puzzles and hidden patterns.
Fun Fact
: She loves to read number jokes and games.
