Place Value and Face Value: Rules, Examples and Tricks

Place Value and Face Value describe two different ways to read a digit in a number. Face value is the digit itself, while place value depends on its position and the value of that position. In 58,406, the face value of 8 is 8, and its place value is 8,000 because it is in the thousands place.

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What Are Place Value and Face Value?

Face value is the digit as it appears in a number. Place value is the value obtained by multiplying the digit by the value of its position.

In the decimal system, positions to the left of the decimal point have values 1, 10, 100, 1,000 and so on. Positions to the right have values 1/10, 1/100, 1/1,000 and so on. For 7,532, the digit 5 has face value 5 and place value 500.

Place Value and Face Value Formula & Tricks

Important Formulas

Place value of a digit
Place value = Digit × Value of its position

For the digit 6 in 46,218, the position value is 1,000, so its place value is 6 × 1,000 = 6,000.

Place value using powers of 10
Place value = d × 10ⁿ

Here, d is the digit and n is the number of places from the units position toward the left. For example, the hundreds position has n = 2.

Decimal place value
Place value = d × 10⁻ⁿ

For digits to the right of the decimal point, n is 1 for tenths, 2 for hundredths, 3 for thousandths and so on.

Quick Tricks

Face value never changes

The face value of a digit remains the digit itself, regardless of its position in the number.

Example: The face value of 4 in 4,321, 2,456 and 98,104 is 4 in every case.
Count zeroes in the position

For whole-number positions, units, tens, hundreds and thousands have 0, 1, 2 and 3 zeroes respectively. Multiply the digit by 1, 10, 100 or 1,000.

Example: The place value of 7 in 72,615 is 70,000 because 7 is in the ten-thousands position.
Use the difference between place and face value

If a digit d is in a position with value p, then place value − face value = d(p − 1).

Example: For 5 in the hundreds place, the difference is 500 − 5 = 495.

Place Value and Face Value Concepts

Difference Between Place Value and Face Value

Face value identifies the digit, whereas place value identifies the amount represented by that digit in its position.

Face value is always a non-negative digit from 0 to 9. Place value can be 0 when the digit is zero, and it may be a whole-number or decimal value depending on the position.

Example: In 93,704, the face value of 3 is 3 and its place value is 3,000. The face value and place value of 0 in the tens place are both 0.

Place Values in Whole Numbers

Moving one place left in a whole number multiplies the position value by 10.

From right to left, the positions are units, tens, hundreds, thousands, ten-thousands, lakhs and ten-lakhs in the Indian system. Thus, the position values are 1, 10, 100, 1,000, 10,000, 1,00,000 and 10,00,000.

Example: In 6,48,219, the digit 4 is in the ten-thousands place, so its place value is 40,000.

Place Values After the Decimal Point

Moving one place right from the decimal point divides the position value by 10.

The first three decimal positions are tenths, hundredths and thousandths, with values 1/10, 1/100 and 1/1,000. Therefore, a digit's place value becomes smaller as it moves right from the decimal point.

Example: In 12.583, the place value of 5 is 5/10 = 0.5, and the place value of 3 is 3/1,000 = 0.003.

Expanded Form and Place Value

Expanded form expresses a number as the sum of the place values of all its digits.

To write expanded form, multiply each digit by its position value and add the non-zero terms. Zero-valued positions may be omitted from the sum.

Example: 7,406 = 7,000 + 400 + 6. Similarly, 3.204 = 3 + 0.2 + 0.004.

Finding a Digit from Its Place Value

A digit can be found by dividing its place value by the value of its position.

If a digit has place value P and its position value is p, then the digit is P ÷ p. The result must be an integer from 0 to 9.

Example: If the place value is 8,000 and the position is thousands, the digit is 8,000 ÷ 1,000 = 8.

Place Value and Face Value Video Lessons

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Practice Place Value and Face Value Questions

Practise published questions related to this topic.

1Find the greatest number that divides 75, 105 and 150 exactly.→ 2Find the HCF and LCM of the fractions 3/8, 5/12, and 7/18.→ 3What is the square root of 1444?→ 4The ratio of two numbers is 3 : 5 and their Least Common Multiple is 120. What is the sum of the two numbers?→ 5Simplify the following expression: √((0.6859 × 0.1156 × 0.64000)/(0.289 × 0.1600 × 0.54872)) (Correct your answer up to three decimal places)→ 6Find the smallest number which when increased by 10 is completely divisible by 12, 15, 18 and 20.→ 7What is the Highest Common Factor of 20, 30 and 50?→ 8156 chips and 234 toffees are to be distributed among maximum number of boys. Each boy gets the same number of chips. Each boy get the same number of toffees. How many chips does each boy get?→ 96336 is divisible by 9. What should be added to or subtracted from this number so that it will be divisible by 11?→ 10Three numbers are in the ratio 3 : 2 : 13, and their LCM is 2574. Their HCF is:→

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Quick Revision Notes

Quick Revision Points

Remember these rules while solving place value and face value questions.

  • Face value is the digit itself and does not depend on position.
  • Place value = digit × position value.
  • The units position has value 1; each position to the left is 10 times the previous position.
  • The first three positions after the decimal point are tenths, hundredths and thousandths.
  • The place value of zero is always zero, even when zero holds a position in the number.
  • Expanded form is the sum of the place values of the digits.
  • Digit = place value ÷ position value.
  • For a digit d in position value p, place value − face value = d(p − 1).

Place Value and Face Value FAQs

What is the face value of 9 in 49,825?

The face value is 9 because face value is the digit itself.

What is the place value of 9 in 49,825?

The place value is 9,000 because 9 is in the thousands place.

What is the place value of 6 in 0.064?

The place value is 0.06, or 6/100, because 6 is in the hundredths place.

How do you find the difference between the place value and face value of a digit?

Subtract the face value from the place value. For 7 in the hundreds place, the difference is 700 − 7 = 693.

What is the place value of zero in 5,008?

Its place value is 0. The zero occupies the hundreds and tens positions, but zero multiplied by either position value remains 0.

How is 8,305 written in expanded form?

8,305 = 8,000 + 300 + 5. The zero in the tens position contributes nothing to the sum.

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