Rounding Calculator
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A rounding calculator keeps the digits up to a chosen place and looks at the next digit to decide: 5 or more rounds up, 4 or less keeps the digit. For example, 1,234.5678 rounded to the nearest hundredth is 1,234.57 (the deciding digit is 7), and to 3 significant figures it is 1,230.
Rounding to significant figures for science or chemistry? The Significant Figures Calculator also counts sig figs and does sig-fig arithmetic.
Compare all 9 rounding methods
| Method | 1,234.5678 → |
|---|---|
| Half away from zero | 1,234.57 |
| Half up (toward +∞) | 1,234.57 |
| Half down (toward −∞) | 1,234.57 |
| Half to even (banker’s) | 1,234.57 |
| Half toward zero | 1,234.57 |
| Up / ceiling | 1,234.57 |
| Down / floor | 1,234.56 |
| Toward zero (truncate) | 1,234.56 |
| Away from zero | 1,234.57 |
Show steps
- Find the rounding placeRounding to the nearest hundredth means keeping digits down to the hundredths place (steps of 0.01).
- Find the two candidates1,234.5678 lies between 1,234.56 and 1,234.57. The halfway point is 1,234.565.
- Look at the deciding digitThe first dropped digit is 7, so the number is more than halfway.
- Apply the method: Half away from zeroRound to the nearer candidate, 1,234.57. (The method only matters for exact ties: ties go away from zero (up for positives, down for negatives).)
- Write the answer1,234.57 (keep trailing zeros: they show the precision).
Related: significant figures calculator · scientific notation converter · percent error calculator
How to use the rounding calculator
- Type the number. Negatives, long decimals and e notation such as 1.25e-6 all work, up to 100 digits.
- Choose what to round to: a place value from millions to millionths, a number of decimal places (0 to 20), a number of significant figures (1 to 20), or the nearest multiple of any step, such as 0.05 or 25.
- Choose a rounding method. The standard school rule (half away from zero) is selected; the other eight methods only differ in how they treat exact halves or whether they always move in one direction.
- Read the answer, the highlighted digits, the number line and the steps. Open “Compare all 9 rounding methods” to see every result side by side.
Use Round a list to round many numbers with the same rule and compare the totals, and Count sig figs to see which digits of a written number are significant.
Rounding rules, step by step
- Find the rounding place (for the nearest hundredth, the second digit after the decimal point).
- Look at the deciding digit, the first digit to its right.
- If it is 5 or more, add 1 to the rounding digit (carrying if it is a 9). If it is 4 or less, leave the rounding digit alone.
- Drop the digits after the rounding place. In the whole-number part, replace them with zeros so the place values stay correct.
Example: round 838.274 to each place. Nearest hundred: 800. Nearest ten: 840. Nearest tenth: 838.3. Nearest hundredth: 838.27. A carry can ripple: 9.995 to the nearest hundredth is 10.00, and the trailing zeros stay because they show the precision.
Rounding methods and negative numbers
Most of the time every method agrees. They differ in two cases: exact halves, and methods that always move one way. This table shows each method rounding to a whole number:
| Method | 2.5 | 3.5 | −2.5 | 2.3 | −2.3 |
|---|---|---|---|---|---|
| Half away from zero (standard) | 3 | 4 | −3 | 2 | −2 |
| Half up (toward +∞) | 3 | 4 | −2 | 2 | −2 |
| Half down (toward −∞) | 2 | 3 | −3 | 2 | −2 |
| Half to even (banker’s) | 2 | 4 | −2 | 2 | −2 |
| Half toward zero | 2 | 3 | −2 | 2 | −2 |
| Up / ceiling | 3 | 4 | −2 | 3 | −2 |
| Down / floor | 2 | 3 | −3 | 2 | −3 |
| Toward zero (truncate) | 2 | 3 | −2 | 2 | −2 |
| Away from zero | 3 | 4 | −3 | 3 | −3 |
Watch the negatives. “Half up” can mean two different things: toward +∞ (so −2.5 becomes −2) or away from zero (so −2.5 becomes −3, the usual school answer). Ceiling always moves toward +∞, so −2.3 becomes −2, while floor moves toward −∞, so −2.3 becomes −3. Banker’s rounding sends ties to the even neighbour (2.5 → 2, 3.5 → 4), so rounding errors do not pile up in one direction; it is the default rounding mode of IEEE 754 floating-point arithmetic and of Python’s round() function.
Decimal places and significant figures
Decimal places count digits after the decimal point. Significant figures count from the first non-zero digit, wherever the decimal point is. That makes significant figures the right choice for very large and very small measurements:
- 0.004876 to 3 significant figures is 0.00488 (4.88 × 10⁻³); to 3 decimal places it would be 0.005.
- 1,234.5678 to 3 significant figures is 1,230 (1.23 × 10³).
- 9.99 to 2 significant figures is 10, written 1.0 × 10¹ to show both figures.
- 0.9999 to 2 significant figures is 1.0.
A trailing zero in a whole number such as 1,230 is ambiguous: it may be a placeholder or a measured digit. Scientific notation removes the doubt.
Counting significant figures
- Non-zero digits always count: 457 has 3.
- Zeros between non-zero digits count: 4,005 has 4.
- Leading zeros never count: 0.0045 has 2.
- Trailing zeros count only with a decimal point: 45.00 has 4, 1,500.00 has 6, but 800 has 1 (up to 3 if the zeros were measured).
Significant figures in calculations
| Operation | Rule | Example |
|---|---|---|
| Add or subtract | Keep the fewest decimal places | 12.11 + 0.3 = 12.41 → 12.4 |
| Multiply or divide | Keep the fewest significant figures | 4.56 × 1.4 = 6.384 → 6.4 |
Round only once, at the end. Rounding in the middle of a calculation lets small errors grow. Exact counts (12 eggs) and defined constants do not limit the figures.
Estimation tips
- Round to the leading digit for a fast check: 48,751 × 3.9 is about 50,000 × 4 = 200,000.
- For a shopping total, round prices to whole dollars: 19.99 + 4.95 + 7.49 dollars is about 20 + 5 + 7 = 32 (exact: 32.43).
- Rounding some numbers up and others down makes the errors cancel; the Round a list tab shows the sum of rounded values next to the exact sum.
- For money and measurements, decide the precision first (cents, millimetres), then round once.
Tricky cases
- 0.0049 to the nearest hundredth is 0.00, not 0.01: the deciding digit is 4.
- 1.005 to 2 decimal places is 1.01 here. Some software shows 1.00 because 1.005 is stored in binary as slightly less than 1.005; this calculator uses exact decimal arithmetic.
- Rounding to the nearest 0.05: 7.43 lies between 7.40 and 7.45 and is closer to 7.45.
- Never round in two stages: 2.346 to the nearest tenth is 2.3, but rounding to 2.35 first and then to 2.4 is wrong.
Rounding practice quiz: 10 questions
Test yourself with 10 multiple-choice questions. Choose an answer and press Submit to see if you are right and why. Your score appears at the end.
The hundreds digit is 7 and the deciding digit (tens) is 6, so round up to 4,800.
The thousandths digit is 8 and the next digit is 4, so it stays: 0.078.
Count from the first non-zero digit: 3, 6, 2. The next digit is 1, so 0.00362.
9.96 rounds up and carries: 10. Written as 1.0 × 10¹ it clearly has 2 significant figures.
4.5 is exactly halfway; banker's rounding picks the even neighbour, 4.
Ceiling moves toward the larger value. On the number line −3 is to the right of −3.8.
Leading zeros do not count; 5, 0, 2 and the trailing 0 after the decimal point do.
23.38 lies between 23.25 and 23.50; it is 0.12 away from 23.50 and 0.13 from 23.25.
Quiz complete
Frequently asked questions
How do you round to 3 significant figures?
Start at the first non-zero digit and count three digits. Look at the fourth: 5 or more rounds the third up, otherwise keep it. 0.004876 becomes 0.00488 and 3.14159 becomes 3.14.
How do you round a negative number?
With the standard rule, round the size of the number and keep the sign: −2.5 → −3 and −2.4 → −2. Ceiling and "half up toward +∞" move toward the larger value instead, so −2.5 → −2 with half up.
What is banker's rounding?
Banker's rounding (round half to even) sends exact halves to the even neighbour: 2.5 → 2, 3.5 → 4, 0.125 → 0.12 to two decimals. Over many numbers the ups and downs balance.
How many significant figures does 800 have?
Usually one, because the trailing zeros may be placeholders. Write 800. or 8.00 × 10² if all three digits were measured.
How many significant figures does 1500.00 have?
Six. The decimal point and the zeros after it show the measurement was taken to the hundredths.
Do significant figures apply to addition?
Addition and subtraction follow decimal places, not significant figures: keep as many decimal places as the least precise number. 12.11 + 0.3 = 12.4.
Related calculators
- Significant figures calculator: count sig figs and apply them in calculations.
- Scientific notation converter: write rounded values as a × 10ⁿ.
- Percent error calculator: see how much rounding changed a value.
- Fraction, decimal and percent calculator: convert before rounding.
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