How rounding works
Rounding replaces a number with a simpler one that is close in value. To round, find the place you are rounding to, then look at the digit immediately to its right:
- If that digit is 5 or more, round up: add one to your place.
- If it is 4 or less, round down: leave your place as it is.
- Drop or zero out every digit after your place.
Examples
| Number | Round to | Result |
|---|
| 1,234.5678 | Hundredths | 1,234.57 |
| 1,234.5678 | Whole number | 1,235 |
| 1,234.5678 | Hundreds | 1,200 |
| 0.0012345 | 3 significant figures | 0.00123 |
Rounding rules compared
- Round half up: the method taught in school. Halves round away from zero.
- Round half to even: halves go to the nearest even digit. Used in finance and statistics so that rounding errors cancel out over many numbers.
- Round up (ceiling): always goes to the next value up. Useful for "how many boxes do I need".
- Round down (floor): always drops the extra. Useful for "how many full sets can I make".
Last reviewed October 2026.
Frequently asked questions
How do I round to the nearest hundredth?
Look at the thousandths digit, the third digit after the decimal point. If it is 5 or more, add one to the hundredths digit; otherwise leave it. Then drop everything after the hundredths. 3.4567 rounds to 3.46.
What happens when the digit is exactly 5?
With standard rounding (round half up), 5 always rounds up: 2.5 becomes 3. With round half to even, also called banker's rounding, it goes to the nearest even digit: 2.5 becomes 2 and 3.5 becomes 4. This avoids a slight upward bias when rounding many numbers.
How do negative numbers round?
With standard rounding the calculator rounds halves away from zero, so −2.5 becomes −3. Rounding up always moves toward positive infinity (−2.1 becomes −2), and rounding down moves toward negative infinity (−2.1 becomes −3).
What are significant figures?
Significant figures are the digits that carry meaning about precision, starting from the first non-zero digit. 0.004560 has four significant figures: 4, 5, 6 and the final 0. Rounding 0.0012345 to three significant figures gives 0.00123.
Why does 1.005 sometimes round to 1.00 in other calculators?
Computers store many decimals as tiny binary approximations, so 1.005 may really be stored as 1.00499999… This calculator shifts the decimal point using the exact digits you typed, so 1.005 correctly rounds to 1.01.