When learning about numbers, two key concepts often come up: place value and face value. Though they sound similar, they represent different ideas in mathematics. Understanding the difference between these two terms is essential for mastering number systems and performing arithmetic operations.
What is Place Value?
Place value refers to the value a digit has based on its position in a number. In any multi-digit number, the value of each digit depends on where it is located. As you move from right to left in a number, the place value increases by a factor of ten.
For example, in the number 6,789:
- 6 is in the thousands place, so its place value is 6,000.
- 7 is in the hundreds place, so its place value is 700.
- 8 is in the tens place, so its place value is 80.
- 9 is in the ones place, so its place value is 9.
The place value gives meaning to the digit’s position in a number, showing its contribution to the total value of the number.
What is Face Value?
Face value refers to the actual value of the digit itself, regardless of its position in the number. No matter where the digit is located, its face value remains the same.
Let’s revisit the same number, 6,789:
- The face value of 6 is 6.
- The face value of 7 is 7.
- The face value of 8 is 8.
- The face value of 9 is 9.
As you can see, the face value is simply the digit itself, unaffected by its place in the number.
Difference Between Place Value and Face Value
The below table lists the key differences between place value and face value.
Let’s take a larger number for a clearer understanding. Consider the number 23,684:
Place Value:
- The place value of 2 is 20,000 (it is in the ten-thousands place).
- The place value of 3 is 3,000 (it is in the thousands place).
- The place value of 6 is 600 (it is in the hundreds place).
- The place value of 8 is 80 (it is in the tens place).
- The place value of 4 is 4 (it is in the ones place).
Face Value:
- The face value of 2 is simply 2.
- The face value of 3 is 3.
- The face value of 6 is 6.
- The face value of 8 is 8.
- The face value of 4 is 4.
Examples in the Indian and International Number Systems
The concepts of place value and face value apply to both the Indian and International number systems, though the grouping of numbers may differ.
Indian Number System Example
For the number 35,78,129:
- The place value of 3 is 30,00,000 (thirty lakhs).
- The face value of 3 is simply 3.
International Number System Example
For the number 3,578,129:
- The place value of 3 is 3,000,000 (three million).
- The face value of 3 is still 3.
Practice
Take the number 54,321.
- What is the place value of 5?
- What is the face value of 5?
- What is the place value of 4?
- What is the face value of 4?
Answers
- 50,000
- 5
- 4,000
- 4
Understanding the difference between place value and face value is an important step in mastering numbers. Place value shows how a digit’s position affects its overall value in a number, while face value remains constant, representing the digit itself.
Practice Quiz on Place Value and Face Value
FAQs on Place Value and Face Value
- Place value determines the overall size or value of the number, while face value only refers to the specific digit itself.
- Example: Changing the placements of the digits in 543 to 345 significantly changes the number’s value, even though the face values remain the same.
- Yes, for example, in 4,782 the face value of 8 is greater than 7, but the place value of 8 (tens place, i.e., 80) is less than the place value of 7 (hundreds place, i.e., 700).
- Shifting a digit one place to the left increases its place value by ten times.
- Example: If 3 in the tens place (value 30) is shifted to the hundreds place, its new place value becomes 300.
- Yes, place value extends to decimals. For example, in the number 12.34, 3 is in the tenths place (value 0.3), and 4 is in the hundredths place (value 0.04).
- No, the face value is always a non-negative digit (0 to 9) since it only represents the numeral itself.