Place Value Calculator
Find the place value of every digit in a number — ones, tens, tenths, and beyond — with a digit-by-digit table, word form, and an addition check.
What is place value?
Place value is what a digit is worth because of where it sits. The same digit means different amounts in different positions: the 5 in 50 is worth 50, but the 5 in 0.05 is worth five hundredths.
The place value names
Each position is a power of ten. Going left of the decimal point: ones, tens, hundreds, thousands, ten thousands, and up. Going right: tenths, hundredths, thousandths, and down.
Worked example: 958.275
| Digit | Place | Value |
|---|---|---|
| 9 | hundreds | 900 |
| 5 | tens | 50 |
| 8 | ones | 8 |
| 2 | tenths | 0.2 |
| 7 | hundredths | 0.07 |
| 5 | thousandths | 0.005 |
Adding the values back: 900 + 50 + 8 + 0.2 + 0.07 + 0.005 = 958.275.
Large and small numbers
Place value scales without limit. In 1987654321 the leading 1 is in the billions place, worth 1000000000. In 0.123456789 the final 9 is in the billionths place, worth 0.000000009.
Digit versus place value
The digit is the symbol; the place value is what it is worth in position. Multiply the digit by its place to get its value.
Common mistakes
- Expecting a "units" place to the right of the decimal point.
- Confusing the digit with the value it holds.
- Miscounting decimal places when naming tenths, hundredths, thousandths.
Place value underlies expanded form and every column method, including long addition.
Frequently asked questions
- What is place value?
- Place value is the value a digit holds because of its position. In 958.275 the 9 is in the hundreds place and is worth 900, while the 5 to the right of the decimal point is in the thousandths place and is worth 0.005.
- What are the place value names?
- Going left from the decimal point they are ones, tens, hundreds, thousands, and so on. Going right they are tenths, hundredths, thousandths, and so on. Each step is ten times larger going left or ten times smaller going right.
- How do you find the value of a digit?
- Multiply the digit by its place value. In 958.275 the 2 is in the tenths place, so its value is 2 times 0.1, which is 0.2.
- Is there a units place after the decimal point?
- No. The place just left of the decimal point is the ones place, and there is no separate "units" place to the right. To the right you go straight into tenths, hundredths, and thousandths.
- What is the difference between a digit and its place value?
- The digit is just the symbol, like 5. Its place value is what that digit is worth in its position — the 5 in 50 is worth 50, while the 5 in 0.05 is worth five hundredths.
- How do decimal place values work?
- They mirror the whole-number places across the decimal point. Tenths are one place right, hundredths two, thousandths three, each ten times smaller than the last, so 0.275 is 0.2 plus 0.07 plus 0.005.
- Why does place value matter?
- Every written arithmetic method depends on it. Lining up digits by place value is what makes column addition, subtraction, long multiplication, and rounding work.