Place Value Calculator

Enter a number and choose a digit's position to find its face value, its place value (digit × 10ⁿ), and the full expanded form of the number.

Quick Facts

Place value formula
Place value = digit × 10ⁿ
n counts positions from the ones place: positive to the left, negative to the right of the decimal point.
Face value
Just the digit, 0-9
Face value never changes; place value depends entirely on position.
Expanded form
Sum of every digit's place value
Example: 4,507.62 = 4,000 + 500 + 7 + 0.6 + 0.02.

Your Results

Calculated
Face value (digit)
-
The digit itself, 0-9
Place value
-
Digit × 10ⁿ
Place name
-
Position of the selected digit
Expanded form
-
Number written as a sum of place values

Ready

Enter a number and choose a digit position, then press Calculate.

How the Place Value Calculator works

Our number system is a base-10 positional (place value) system: the same digit represents a different amount depending on where it sits in a number. The value contributed by a digit is called its place value, and it always equals the digit multiplied by a power of 10: place value = digit × 10ⁿ, where n is the digit's position counted from the ones place — positive powers (1, 10, 100, 1,000, …) for whole-number places to the left, and negative powers (0.1, 0.01, 0.001, …) for decimal places to the right.

Formula and method

Pick out the digit at the position you care about, then multiply it by 10 raised to that position's power. For example, in 4,507.62 the digit 5 sits in the hundreds place (n = 2), so its place value is 5 × 10² = 500. The digit 6 sits in the tenths place (n = −1), so its place value is 6 × 10⁻¹ = 0.6. This calculator locates the digit at the position you select — from hundred millions down to ten-thousandths — and reports both its face value and its place value, along with the number's full expanded form (every digit's place value added together).

Face value vs. place value

These two terms are easy to mix up. The face value of a digit is just the digit itself, 0 through 9, regardless of where it appears. The place value is what that digit is actually worth in the number, based on its position. In 4,507.62, the face value of the 5 is simply "5," but its place value is 500 because it occupies the hundreds position — move that same digit to the tens place and its place value drops to 50.

Common sources of error

  • Confusing face value and place value: the digit "5" is always face value 5, but its place value depends entirely on position.
  • Miscounting decimal positions: the first digit after the decimal point is tenths (10⁻¹), not ones-and-a-half — count from the decimal point outward: tenths, hundredths, thousandths.
  • Dropping a leading or trailing zero: a zero digit still occupies a place (and has place value 0), so don't skip it when reading positions from a number like 4,507.

Applications

Place value underlies rounding (you round based on the digit in the next place over), scientific notation, currency and unit conversions, and how calculators and computers internally represent numbers. Teachers use expanded form to show students why "carrying" and "borrowing" work in addition and subtraction, since those operations are really just regrouping between place values.

Frequently Asked Questions

What is the difference between face value and place value?
Face value is simply the digit itself (0-9), with no regard to where it sits in the number. Place value is the digit multiplied by the power of 10 assigned to its position, so the same digit can be worth very different amounts depending on where it appears. For example, in 4,507.62 the face value of the 5 is 5, but its place value is 500 because it sits in the hundreds position.
How do you find the place value of a digit after the decimal point?
Digits to the right of the decimal point use negative powers of 10: the first digit is tenths (10⁻¹), the second is hundredths (10⁻²), the third is thousandths (10⁻³), and so on. Multiply the digit by that power of 10, so a 6 in the tenths place equals 6 × 10⁻¹ = 0.6.
What is expanded form and how is it related to place value?
Expanded form rewrites a number as the sum of each digit's place value. For 4,507.62 that is 4,000 + 500 + 7 + 0.6 + 0.02. Adding those place values back together reproduces the original number, which is a quick way to check your place value work.
How does moving a digit one position change its place value?
Each step to the left multiplies a digit's place value by 10, and each step to the right divides it by 10, because the base-10 place value system is built entirely on consecutive powers of 10.

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