Round to the Nearest Thousandth Calculator
Round decimal numbers to the nearest thousandth (three decimal places) with step-by-step explanations
Round Your Number
Enter any decimal number to round to the nearest thousandth
Example Calculations
9 ≥ 5, so round up
9 ≥ 5, so round up
1 < 5, so round down
4 < 5, so round down
6 ≥ 5, so round up
5 ≥ 5, so round up
Rounding Rules
Round Up
If ten-thousandths digit ≥ 5
Add 1 to thousandths place
Round Down
If ten-thousandths digit < 5
Keep thousandths place the same
Place Value Guide
Example: In 3.4567, the thousandths place is 6, ten-thousandths is 7
Understanding Rounding to the Nearest Thousandth
What is the Thousandths Place?
The thousandths place is the third digit after the decimal point. It represents one-thousandth (1/1000) of a whole unit. When rounding to the nearest thousandth, we look at the ten-thousandths place (fourth digit after decimal) to decide whether to round up or down.
Rounding Rules
- •If ten-thousandths digit is 5, 6, 7, 8, or 9: round UP
- •If ten-thousandths digit is 0, 1, 2, 3, or 4: round DOWN
- •Result always has exactly three decimal places
Step-by-Step Process
- 1. Identify the thousandths place (3rd digit after decimal)
- 2. Look at the ten-thousandths place (4th digit after decimal)
- 3. Apply the rounding rule based on ten-thousandths digit
- 4. Write the result with three decimal places
Common Examples
Special Cases and Advanced Examples
Cascade Rounding
When the digit to round is 9, it changes to 0 and the preceding digit increases by 1. This can cascade through multiple digits.
Numbers with Fewer Decimals
If a number has fewer than three decimal places, you can add trailing zeros or leave it as is.