Rounding to a place value
Rounding replaces a number with a simpler one close to it, keeping a chosen number of digits. You round prices to the cent, measurements to the millimeter, statistics to one decimal and large figures to the nearest thousand. This calculator rounds a number to every common place value at once, using the method you choose.
The three methods
- To the nearest (half up): look at the first digit you drop. If it is 5 or more, increase the last kept digit by one; otherwise keep it. Halves are rounded away from zero, so 2.5 becomes 3 and −2.5 becomes −3.
- Round down (floor): always go to the lower value: 3.99 becomes 3, and −3.2 becomes −4.
- Round up (ceiling): always go to the higher value: 3.01 becomes 4, useful when you need enough of something, such as boxes or buses.
Worked example: 1,234.5678
| Place | Result |
|---|---|
| Nearest thousand | 1,000 |
| Nearest hundred | 1,200 |
| Nearest ten | 1,230 |
| Nearest whole number | 1,235 |
| Nearest tenth | 1,234.6 |
| Nearest hundredth | 1,234.57 |
| Nearest thousandth | 1,234.568 |
For the nearest hundredth, the kept digits are 1,234.56 and the next digit is 7, so the 6 becomes 7.
Rounding to a multiple
Sometimes you round to a step rather than a place: prices to the nearest $0.05, times to the nearest 15 minutes, lumber to the nearest 2 feet. The rule is the same: divide by the step, round to a whole number, multiply back. 1,234.5678 to the nearest 5 is 1,235; 7.38 to the nearest 0.25 is 7.50, because 7.38 ÷ 0.25 = 29.52 rounds to 30.
Common pitfalls
- Round once, at the end. Rounding 2.449 to 2.45 and then to 2.5 gives the wrong answer; rounding 2.449 directly to one decimal gives 2.4.
- Totals may not add up. Rounded parts of a whole can sum to 99% or 101%. That is normal; say so in a note or adjust the largest item.
- Banker’s rounding. Some software, including Python’s round() and many accounting systems, rounds halves to the nearest even digit (2.5 → 2, 3.5 → 4) to avoid bias. This calculator rounds halves away from zero, as taught in school.
- Money. Tax and invoices are usually rounded to the cent at each line or on the total, depending on local rules; check which one your software uses.
- Significant figures count digits from the first non-zero one: 0.004567 to 2 significant figures is 0.0046, while to 2 decimals it is 0.00.