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Place Value and Face Value are fundamental concepts in mathematics. Place Value and Face Value help us understand the working of the numbers in a better way. Although they might sound similar and create confusion in your head, they are simple to understand and they represent different ideas.
Read the article below for a better understanding of the Place Value and Face Value and the difference between them.
Place Value and Face Value Definition
Place Value refers to the value a digit holds based on its position within a number. For instance, in the number 4,587, the digit 5 is in the “hundreds” place, so its place value is 500. This means that the value of the digit changes depending on where it is located in the number.
Face Value, on the other hand, is simply the value of the digit itself, regardless of its position. In the number 4,587, the face value of the digit 5 is 5. This value remains the same no matter where the digit appears in the number.
Place Value Meaning
Place Value is the value of each digit in a number, determined by its position. To find the place value, you multiply the digit by the value of its place in the number.
Example: Let’s find the place value of each digit in the number 3279.
- Thousands Place: The digit 3 is in the thousands place. Its place value is calculated as: 3 × 1000=3000. So, the place value of 3 is 3000.
- Hundreds Place: The digit 2 is in the hundreds place. Its place value is: 2 × 100=200. So, the place value of 2 is 200.
- Tens Place: The digit 7 is in the tens place. Its place value is: 7 × 10=70. So, the place value of 7 is 70.
- Ones Place: The digit 9 is in the ones place. Its place value is: 9 × 1=9. So, the place value of 9 is 9.
Face Value Meaning
Face Value refers to the actual value of a digit in a number no matter at which position it is placed. Essentially, it’s the digit itself. The face value of a digit is without adjustments or calculations based on its location.
Example: Let’s find the face value of each digit in the number 3279.
- Face Value of 3: The face value is 3.
- Face Value of 2: The face value is 2.
- Face Value of 7: The face value is 7.
- Face Value of 9: The face value is 9.
Also Check: Place Value Worksheets
Expanded Form of Place Value and Face Value
Expanded Form is a way to express a number as the sum of the values of its digits, based on their place value. This expansion helps us highlight and understand the contribution of each digit to the overall number.
Example: Let’s break down the number 432 into its expanded form.
Place Value: is the value of each digit in a number, determined by its position.
- Place Value of 4: The digit 4 is in the hundreds place, so its place value is 400.
- Place Value of 3: The digit 3 is in the tens place, so its place value is 30.
- Place Value of 2: The digit 2 is in the ones place, so its place value is 2.
- In expanded form, the number 432 can be written as: 432 = 400 + 30 + 2
- This form shows how each digit contributes to the total value of the number based on its place value.
Face Value: In contrast to the place value, the face value of each digit remains the same regardless of its position.
- The face value of 4 is 4.
- The face value of 3 is 3.
- The face value of 2 is 2.
Thus, while the expanded form focuses on how digits are combined according to their place values, face value simply reflects the digit itself.
Place Value Chart
A Place Value Chart is a useful tool for organizing digits in a number to accurately determine their place values. It helps ensure that digits are aligned correctly and makes it easier to understand the value of each digit in a number. There are two main types of place value charts:
Indian Place Value Chart
The Indian Place Value Chart is based on the Indian numeral system and is commonly used in South Asia. It organizes numbers into periods separated by commas as follows:
- Units Period: Ones, Tens, Hundreds
- Thousands Period: Thousands, Ten Thousands, Lakhs (Hundred Thousands), Ten Lakhs (Million)
- Crores Period: Crores (Ten Million), Ten Crores (Hundred Million)
For example, in the number 12,34,567:
12,34,567 is read as 12 Lakhs, 34 Thousand, 567.
International Place Value Chart
The International Place Value Chart is based on the internationally accepted numeral system and is used worldwide. It divides numbers into periods separated by commas as follows:
- Units Period: Ones, Tens, Hundreds
- Thousands Period: Thousands, Ten Thousands, Hundreds Thousands
- Millions Period: Millions, Ten Millions, Hundred Millions
- Billions Period: Billions, Ten Billions, Hundred Billions
For example, in the number 12,345,678: 12,345,678 is read as 12 Million, 345 Thousand, 678.
Also Check: International System of Numeration
Key Differences between Place Value and Face Value
- In the Indian system, commas are placed after every two digits starting from the right after the first three digits (e.g., 1,23,456).
- In the International system, commas are placed after every three digits (e.g., 123,456).
- The Indian system uses terms like Lakhs and Crores, whereas the International system uses terms like Thousands, Millions, and Billions.
Difference Between Place Value and Face Value
Place Value and Face Value are fundamental concepts in understanding numbers, but they represent different aspects of a digit’s contribution to a number. The table given below displays the difference between Place Value and Face Value.
| Aspect | Place Value | Face Value |
| Definition | The value is represented by a digit based on its position. | The actual digit itself. |
| Calculation | Calculated by multiplying the digit by the value of its position. | Always the digit itself. |
| Dependence | Depends on the digit’s position in the number. | Independent of the digit’s position. |
| Example | In 452, a place value of 5 is 5×10=50. | In 452, face value of 5 is 5. |
| Zeros | The place value of 0 is 0. | The face value of 0 is also 0. |
| Change with Position | Changes as the position of the digit changes (ones, tens, hundreds, etc.). | Remains the same regardless of position. |
| Value Representation | Represents the digit’s contribution based on its position. | Represents the digit’s actual value. |
Place Value and Face Value Practice Questions
On the basis of your understanding of the concepts, solve the following questions.
- Determine the place value and face value of the digit 7 in the number 8,734.
- Find the place value of the digit 6 in the number 56,789. What is its face value?
- Write the number 2,048 in expanded form. Include the place value of each digit.
- In the number 9,501, what is the place value of the digit 9? What is the face value of the digit 0?
- For the number 4,302, determine the face value of each digit and then calculate their respective place values.
- Expand the number 7,560 into its place values. What is the place value of the digit 5?
- In the number 15,382, find the place value of the digit 3. What is the face value of the digit 8?
- Given the number 93,468, write down the place value and face value of the digit 4.
FAQs on Place Value and Face Value
What is the difference between place value and face value?
Place Value refers to the value of a digit based on its position in a number. For example, in the number 345, the place value of 4 is 40 because it is in the tens place. Face Value is simply the digit itself, regardless of its position. In the same number, the face value of 4 is just 4.
How do you calculate the place value of a digit?
To calculate the place value of a digit, multiply the digit by the value of its position. For instance, in the number 5,872, the place value of the digit 8 (which is in the hundreds place) is 8×100=800.
How does place value change as you move left in a number?
As you move left in a number, each digit’s place value increases by a factor of ten. For example, in the number 7,245, the digit 2 is in the hundreds place (place value of 200), while the digit 4 is in the thousands place (place value of 4,000). Each position to the left increases the place value by a factor of ten.
