Rounding Calculator: Decimals, Significant Figures, Nearest 10 or Fraction
Round to decimal places, significant figures, the nearest 10 or 100, or the nearest ½ to 1/64, with a choice of tie rule.
Inputs
- Working
- 2.675 × 100 = 267.5 → 268 ÷ 100 = 2.68
- Original
- 2.675
- Decimal places
- 2
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What each Rounding input means
- Number
- The number to round. Decimals and negatives are fine; a negative rounds by the mirrored rule, so −2.5 to a whole number is −3 when 5 rounds up (away from zero).
- Round to
- Decimal places for money and measurements, significant figures for science, the nearest 10, 100 or any step for estimates, or the nearest fraction for tape-measure readings.
- How many places or figures
- How many decimal places, or how many significant figures, depending on the mode. 0 decimal places rounds to a whole number. The answer keeps trailing zeros, so 2.96 to one place reads 3.0.
- Nearest
- The step to round to in 'nearest' mode: 10, 100, 1000, 0.5, 0.25, 5 — any positive number. Rounding to the nearest 0.05 is how cash totals are rounded where one- and two-cent coins have been withdrawn.
- Nearest
- The fraction for nearest-fraction mode, from halves down to sixty-fourths. Sixteenths suit a tape measure; thirty-seconds and sixty-fourths suit drill bits and machining.
- When the dropped digit is exactly 5
- Only matters when the digit dropped is exactly 5 with nothing after it. School arithmetic rounds it up; science and banking round to the even neighbour, so ties don't push totals upward.
Rounding formula
decimal places: round(x × 10ⁿ) ÷ 10ⁿ · nearest step: round(x ÷ step) × step · significant figures: keep n digits from the first non-zero one
Rounding keeps the digits that matter and looks at the first one dropped: below 5, the kept digit stays; above 5, it goes up by one. The only real disagreement is about an exact 5. School arithmetic, as in OpenStax Prealgebra, rounds it up — 23,658 to the nearest hundred is 23,700 — and away from zero for negatives. Science, as in OpenStax Chemistry, rounds a lone 5 to whichever neighbour is even, so 92.85 to three significant figures is 92.8; that is also banker's rounding. The page offers both. Besides decimal places it rounds to significant figures (counted from the first non-zero digit), to the nearest 10, 100, 0.5 or any step, and to the nearest fraction such as 1/8 or 1/16 for measurements.
Rounding worked example
2.675 to two decimal places: 2.675 × 100 = 267.5, which rounds up to 268, so 2.68. Rounding the 5 to the even digit instead gives 2.68 too, because 8 is even; 2.665 would go up to 2.67 by the school rule and down to 2.66 by the even rule.
More Rounding examples
OpenStax Chemistry's example, 92.85 to three significant figures by the even rule: the dropped digit is exactly 5, and the kept digit, 8, is already even, so it stays — 92.8. The school rule would give 92.9.
1,234.5678 to the nearest 50: 1,234.5678 ÷ 50 = 24.69, which rounds to 25, and 25 × 50 = 1,250.
2.3 inches to the nearest eighth: 2.3 × 8 = 18.4, which rounds to 18 eighths, simplified to 2 1/4. The rounding error is 0.05 inch.
0.125 to two places by the even rule: 12.5 hundredths sits exactly halfway, and 12 is even, so it rounds down to 0.12. The school rule gives 0.13.
Where the Rounding calculator can give the wrong answer
- A number like 2.675 is stored in binary as 2.67499999…, which makes many calculators round it to 2.67. This page treats anything within a billionth of a 5 as a 5, so it gives the pencil-and-paper answer.
- Significant figures count from the first non-zero digit: 0.004567 to two figures is 0.0046, and 123,456 to three is 123,000.
- Rounding to the nearest fraction gives a mixed number: 3.14159 to the nearest 1/16 is 3 1/8.
- Rounding again and again (2.4449 → 2.445 → 2.45) can give a different answer from rounding once (2.44). Round once from the original.
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Rounding reference table
| Round to | 3.14159 | 2,674.5 | 0.004567 |
|---|---|---|---|
| Whole number, 5 rounds up | 3 | 2,675 | 0 |
| Whole number, 5 rounds to even | 3 | 2,674 | 0 |
| 2 decimal places | 3.14 | 2,674.50 | 0.00 |
| 3 significant figures | 3.14 | 2,670 | 0.00457 |
| Nearest 100 | 0 | 2,700 | 0 |
| Nearest 1/16 | 3 1/8 | 2674 1/2 | 0 |
Rounding FAQ
- Look at the third decimal place: 5 or more rounds the second up, less leaves it. 3.14159 → 3.14; 2.675 → 2.68.
- Count that many digits from the first non-zero digit and round the next. 0.004567 to 2 significant figures is 0.0046; 92.85 to 3 is 92.9 by the school rule or 92.8 by the science rule.
- When the digit dropped is exactly 5, round to the even neighbour: 2.5 → 2, 3.5 → 4. Chemistry courses use it and banks call it banker's rounding, because it doesn't push totals upward the way always rounding 5 up does.
- Choose 'nearest fraction' and 1/16. The page multiplies by 16, rounds, and simplifies: 3.14159 × 16 = 50.27 → 50/16 = 3 1/8.
- Look at the first decimal place: 5 or more rounds up, less than 5 rounds down. 7.5 becomes 8 and 7.49 becomes 7; by the school rule −7.5 becomes −8.
- Keeping one decimal place: 3.14159 becomes 3.1, and 2.96 becomes 3.0. The nearest hundredth keeps two places, and the nearest thousandth three.