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The main difference between face value and place value is that place value refers to the digit's location, whereas face value refers to the real worth of the digit. One must know the basic concepts of the number system for categorising digits into tens, hundreds, and even thousands of groups.
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Key Terms: Place Value, Face Value, Number System
Introduction to Face Value and Place Value
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One needs to use the expanded form of the given number to understand the notion of a face value and place value of an integer. For example, let us consider:
859 = 800 + 50 + 9
= 8 × 100 + 5 × 10 + 9 × 1
Then,
| Digit | Place value | Face value |
|---|---|---|
| 8 | 800 | 8 |
| 5 | 50 | 5 |
| 9 | 9 | 9 |
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Face Value
The value of a digit can indicate the face value of any number. For instance, 9 is the face value of number 9 in number 9564.
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Place Value
The value of every numerical number is known as the place value. We may get its place value by multiplying a number's digit value with its numerical value. For example, since 6 is in the thousands place, we multiply 6 (numerical value) by 1000 (digit value) to get 6000, which is the place value of '6' in the number 56178. We can get the place values of the remaining integers in the number in the same way.
Place Value and Face Value
Properties of Place Value
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- The place value of every one-digit number is the same as and equal to its face value.
(i) The face value and place value of the numbers 1, 2, 3, 4, 5, 6, 7, 8, and 9 are respectively 1, 2, 3, 4, 5, 6, 7, 8, and 9.
(ii) The value of zero (0) in any place is always 0. For example, it can take any position in a number, but its value is always zero.
0’s place value in each number is 0 in 605, 201, 7089, and 359050.
- The ten-place digit in a two-digit number has a place value of 10 times the digit.
As 3 has a place value of 3 x 10 = 30 in 31 and 1 has 1 x 1= 1, the face value of 3 is 3, and value of 1 is 1.
- The digit 9 is at one's position, the digit 1 is at ten's place, and the digit 6 is at hundred's place in the number 619.
As a result, the place value of 9 is 9, 1 is 1 x 10 is 10 and 6 is 6 x 100 = 600
Thus, when a digit's place value is multiplied by the place value of 1, it must be that place.
Example: In 9456,
6: - 6 × 1 = 6
5: - 5 × 10 = 50
4: - 4 × 100 = 400
9: - 9 x 1000 = 9000
- Now, the general rule is that the digit's place value is equal to the product of the place value of one and the digit at that point.
Let us consider an example:
(i) In the given number 359;
9 × 1 = 9. This is because 9 is present at one’s or unit’s place.
5 × 10 = 50, because 5 is placed at ten’s place.
3 × 100 = 300, because 3 is present at hundred’s place.
Difference between Place Value and Face Value of a Number
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The number system in place value goes from 0 through tens, hundreds, thousands, and so 0
| Place Value | Face Value |
|---|---|
| The value provided by a digit in a number per its placement in the numeric value is known as place value. | The true value of an integer in a number is referred to as the face value. |
| To find a number's place value, multiply the digit’s position value by its numerical value. For instance, as 5 is in the tens place, the place value of 4 in the number 748 is (4 x 10) = 40. | A digit's face value is the number itself. The face value of 4 in the number 748, for example, is 4. |
| The place value is found out by the digit's location in the number. | If the digit's location in the number is changed, the face value remains unaffected. |
| A digit's place value is always a single digit, and the place value of each subsequent digit to the left rises by one digit. | A face value of a number is always a single integer. |
Expanded Form
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The extended form of any number can be used to understand the difference between place value and face value. 800 + 60 + 1 is the enlarged version of 861.
By adding the place values of each digit, we can represent a number in expanded form. For example, the place value of 8 is 800 (because it is in the hundreds place), the place value of 6 is 60 (because it is in the tens place), and the place value of 1 is 1 (because it is in the one's place) in the example above. However, the face value of 8 is 8, the face value of 6 is 6, and the face value of 1 is 1. In the same number 861, the face value of 8 is 8, the face value of 6 is 6, and the face value of 1 is 1.
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Things to Remember
- Both the place value and face value of the numbers 1, 2, 3, 4, 5, 6, 7, 8, and 9 are respectively 1, 2, 3, 4, 5, 6, 7, 8, and 9.
- The face value and place value of 0 are always 0.
- The face value of any digits always remains the same.
- Place Value of a digit is given by multiplying to the 10^n, where n is the digit's position in the number from the right side.
- The expanded form helps determine the place value of each digit present in the given number.
Sample Questions
Ques: State the place value of 9 in 9458? (1 mark)
Ans: The place value of 9 in 9458 is 9000
Ques: What is the place value of a number? Please give an example. (2 marks)
Ans: A digit's place value determines where it is put or positioned in a number. It might be in the form of a single unit, tens of units, hundreds of units, and so on. Example: The tenth-place value of 6 in 59648 is 6 x 100 = 600.
Ques: State the face value of 1 in 984156? (1 mark)
Ans: The face value of 1 in 984156 is 1.
Ques: What is the face value of this item? Please give an example. (2 marks)
Ans: The face value of a digit in a number determines the number's overall worth. It makes no difference where the digit is located. The face value of an eight in 189345, for example, is merely 8.
Ques: State the Face value and Place value for each digit 94587. (3 marks)
Ans: 7 is the Face value of 7
Place value of 7 is 7
8 is the Face value of 8
Place value of 8 is 80
5 is the Face value of 5
Place value of 5 is 500
4 is the Face value of 4
Place value of 4 is 4000
9 is the Face value of 9
Place value of 9 is 90000
Ques: What should be the place value and face value 2 and 7 in 259784? (2 marks)
Ans: Place values - 2 is 200000, 7 is 700
Face values - 2 is 2, 7 is 7
Ques: Write two differences between the face value and the place value of a number. (2 marks)
Ans:
| Place Value | Face Value |
|---|---|
| The digit multiplied by hundreds or thousands is called place value, depending on where it is put. | The digit itself present in the number is simply described as face value. |
| By multiplying a digit's value to the digit’s position in which it is found, the place value can be determined. | A digit's face value is always the same, regardless of its position. |
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