A place value calculator breaks a number into its digits and shows what each digit is worth. Type any whole number or decimal and you get a place value chart, the expanded form, and, if you choose a place, the digit in that place, such as the thousands place or the hundredths place.
Use it to check homework on place value, to find the digit in the tens, hundreds or thousands place, or to write a number in expanded form. To check your own steps in other maths, the answer checker compares your answer with the computed result.
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How place value works
Whole number places
Each place to the left of the decimal point is worth ten times the place to its right. The ones place is the first place to the left of the decimal point.
| Place | Value of a 1 in that place |
|---|---|
| Ones | 1 |
| Tens | 10 |
| Hundreds | 100 |
| Thousands | 1,000 |
| Ten thousands | 10,000 |
| Hundred thousands | 100,000 |
| Millions | 1,000,000 |
Decimal places
Each place to the right of the decimal point is worth one tenth of the place to its left.
| Place | Value of a 1 in that place |
|---|---|
| Tenths | 0.1 |
| Hundredths | 0.01 |
| Thousandths | 0.001 |
| Ten-thousandths | 0.0001 |
Tenths, not oneths
The first place to the right of the decimal point is the tenths place. There is no place called oneths, and the decimal places all end in th to show they are parts of a whole.
Digit and value
The digit is the numeral in a place. The value is the digit multiplied by the worth of the place. In 3,482.756, the digit 8 is in the tens place, so its value is 8 × 10 = 80.
Worked examples
Example 1: 3,482.756
| Digit | Place | Value |
|---|---|---|
| 3 | Thousands | 3,000 |
| 4 | Hundreds | 400 |
| 8 | Tens | 80 |
| 2 | Ones | 2 |
| 7 | Tenths | 0.7 |
| 5 | Hundredths | 0.05 |
| 6 | Thousandths | 0.006 |
The expanded form is 3,000 + 400 + 80 + 2 + 0.7 + 0.05 + 0.006.
Example 2: A zero in the thousands place
In 90,516.034 the digit in the ten thousands place is 9 and the digit in the thousands place is 0. A zero holds its place even though it adds nothing to the value.
The expanded form is 90,000 + 500 + 10 + 6 + 0.03 + 0.004.
Example 3: A decimal less than 1
In 0.082, the digit in the tenths place is 0 and the digit in the hundredths place is 8. The expanded form is 0.08 + 0.002.
Frequently asked questions
What is the thousands place?
The thousands place is the fourth place to the left of the decimal point. In 3,482.756 the digit in the thousands place is 3.
What is the hundredths place in 4.592?
The hundredths place is the second place to the right of the decimal point. In 4.592 the tenths digit is 5, the hundredths digit is 9 and the thousandths digit is 2.
What is the difference between place and value?
The place is the position of a digit, such as tens. The value is what that digit is worth there. The digit 8 in the tens place has a value of 80.
How do you write a number in expanded form?
Write the value of each non-zero digit and add them. For 3,482 that is 3,000 + 400 + 80 + 2.
Does a negative sign change the place values?
No. The sign does not change which place a digit is in, so the calculator ignores it.