In mathematics, the main difference between place value and face value lies in their definitions and significance within a number. Place value pertains to the value associated with the position of a digit within a number, while face value represents the actual numerical value of the digit itself, irrespective of its position. Understanding this distinction is crucial in comprehending numerical systems and calculations. Here are several solved examples and frequently asked questions to further clarify the disparity between place value and face value.
The Difference Between Place Value and Face Value is that place value refers to the value of the position of a digit within a number, whereas face value refers to the actual value of the digit itself, regardless of its position within the number.
Table of Contents
What is Place Value?
The Place Value represents the position of a digit in a Number. In other words, The Place Value is the value of each digit in a number. For example: the 4 in 406 represents 400; however, the 4 in 348 represents 40.
Properties of Place Value
The main properties of place value are as follows:
- The place value of every one-digit number is the same as and equal to its face value.
- The position of a digit in a number determines its value.
- In a three-digit number, the place value of the hundred-place digit is 100 times of the digit.
What is Face Value?
The Face Value of a digit in a number is the digit itself. For example, in 456, the face value of 5 is 5; the face value of 4 is 4; the face value of 6 is 6.
Properties of Face Value
The main properties of face value are as follows:
- The face value depends on the position of the digit within the number.
- In 345, the face value of 4 is 4, the face value of 3 is 3, the face value of 5 is 5.
- The numerical value of a digit can vary depending on the base of the number system being used.
Similarities of Place Value and Face Value
- The place value and face value are always equal at ones place.
- Place value and face value represent properties of digits within a number.
- Place value and face value both rely on the positional system of numbers.
Difference between Place Value and Face Value
The major difference between Place value and Face Value are as follows:
| Place Value | Face Value |
| 1. Place value represents the position of a digit in a number. | 1. Face value represents the actual numerical value of a digit. |
| 2. In place value, each digit’s place value is multiplied by a power of 10 according to its position in the number. | 2. Face value remains constant regardless of the digit’s position. |
| 3. The place value of 0 is 0. | 3.The face value of 0 is 0. |
| 4.For example: The place value of 3 in the number 432 is 30 | 4.For example: The face value of 4 in the number 432 is 4. |
| 5.Determines the value of a digit based on its position within the number. | 5.It’s the digit itself, without considering its position within the number. |
| 6. Helps understand the magnitude of a digit within a number. | 6. Helps identify the individual numerical worth of each digit within a number, independent of its position. |
Chart of Place Value and Face Value
A chart of place value and face value helps in understanding the numerical value of each digit in a number.
Here’s a simple example for the number 3456:
| Place Value | Thousands | Hundreds | Tens | Ones |
| Face Value | 3 | 4 | 5 | 6 |
- Place value represents the position of each digit in the number.
- Face value represents the actual value of each digit.
The Indian System of Numeration
In Indian System of Numeration, the place values of digits go in the sequence of Ones, Tens, Hundred, Thousands, Ten Thousands, Lakhs, Ten Lakhs, Crores, Ten Crores and so on.
The International System of Numeration
In International System of Numeration, The place values of digits go in the sequence of Ones, Tens, Hundreds, Thousands, Ten Thousands, Hundred Thousands, Millions, Ten Millions, Hundred Millions, Billions and so on.
Points to Remember
- The face value of a digit is always the same as its place value when it is in the units place.
- The face value and place value of 0 are always 0.
- In multi-digit numbers, zeros act as placeholders to indicate the absence of a digit in a certain place value position. They do not add any value of their own, but they affect the magnitude of the number.
- Expressing a number in expanded form involves breaking it down into its component digits and place values. This help in understanding the value of each digit within the number.
Read more: What is a Number?
Solved example
1. What is the Face value of 5 in 534?
Answer- The Face value of 5 in 534 is 5.
2. What is the Place value of 4 in 453?
Answer- The Place value of 4 in 453 = 4 × 100 = 400.
3. Find the product of Place value of 4 in 5,467 and Place value of 5 in 6,544?
Solution: The Place value of 4 in 5,467= 4 × 100 = 400
And, the Place value of 5 in 6,544 = 5 × 100 = 500
Therefore, their product = 400 × 500 = 2,00,000
4. Find the sum of Place value of 3 in 345 and Face value of 5 in 456?
Solution: The Place value of 3 in 345 = 3 × 100= 300
And, the Face value of 5 in 456 = 5
Therefore, their sum = 300 + 5 = 305
5. Find the Face value and Place value of each digit of 51,209
Solution: The Face value of 9 in 51,209 = 9
The Place value of 9 in 51,209 = 9 × 1 = 9
The Face value of 0 in 51,209 = 0
The Place value of 0 in 51,209 = 0 × 10 = 0
The Face value of 2 in 51,209 = 2
The Place value of 2 in 51,209 = 2 × 100 = 200
The Face value of 1 in 51,209 = 1
The place value of 1 in 51,209 = 1 × 1,000 = 1,000
The Face value of 5 in 51,209 = 5
The place value of 5 in 51,209 = 5 × 10,000 = 50,000
6. Find the difference of Place value of 9 in 987 and Face value of 5 in 453?
Solution: The Place value of 9 in 987 = 9 × 100 = 900
And, the Face value of 5 in 453 = 5
Therefore, their difference = 900 – 5 = 895.
7. What is the expanded form of 456?
Solution: The expanded form of 456 is = 400 + 50 + 6.
8. In the number 26369 write the place values of the two 6s and the sum of these two place values.
Solution: The place value of 6 in the thousands place = 6 × 1000 = 6000
The place value of 6 in the tens place = 6 × 10 = 60
So, the sum of the two place values of 6 = 6000 + 60 = 6060
9. Find the difference between the place value and the face value of the digit 5 in 23,05,981.
Solution: The place value of 5 in 23,05,981 = 5 × 1000 = 5000
And, the face value of 5 in 23,05,981 = 5
Therefore, their difference = 5000 – 5 =4995
10. Find the sum of the place value and the face value of 7 in the number 5,73,851.
Solution: The place value of 7 in 5,73,851 = 7 × 10,000 = 70,000
And, the face value of 7 in 5,73,851 = 7
Therefore, the sum of the place value and face value of 7 = 70,000 + 7 = 70,007
FAQs related to Place Value and Face Value
1. What is Place value?
Answer- Place value of a digit is the value of the position of that digit within the given number.
2. What is Face value?
Answer- The Face value of any digit in the number is the value of the digit itself.
3. Why are Place value and Face value important?
Answer- Understanding Place value and Face value is fundamental to understanding how numbers are structured and how arithmetic operations are performed. It forms the basis for more advanced mathematical concepts and calculations.
4. What is the relationship between Place value and Face value?
Answer- The Place value of a digit depends on its position in a number, while the face value is the actual value of the digit itself.
