Scientists and engineers report numbers to a fixed count of significant figures rather than a fixed number of decimal places, because the count reflects how precise a measurement or calculation really is. A distance of 149,600,000 km and a mass of 0.0001496 kg both have four significant figures, even though one has no decimals and the other has seven. This calculator rounds to any number of significant figures and gives the answer in a form that keeps that precision visible.
How to use the calculator
- Enter a number in standard form (
149,597,870.7) or scientific notation (6.674e-11). - Choose how many significant figures to keep.
- The tape shows the result in standard form, scientific notation and E-notation. If the standard form would hide significant zeros, the scientific form becomes the headline answer.
- The digit display highlights the last digit kept (blue) and the digit that decides the rounding (amber). A table shows the number rounded to several other counts.
How rounding to significant figures works
- Find the first significant digit — the first non-zero digit from the left.
- Count that many digits to the right, including any zeros you pass.
- Look at the next digit. If it is 5 or more, increase the last kept digit by 1; if it is less than 5, leave it.
- Fill or drop. Digits removed to the left of the decimal point become zeros so the number keeps its size; digits to the right of the decimal point are dropped.
Worked example: the astronomical unit
The International Astronomical Union defined the astronomical unit in 2012 as exactly 149,597,870.7 km — the average Earth–Sun distance used in astronomy. Round it to 3 significant figures:
First significant digit: the 1 in the hundred-millions place
Three digits: 1, 4, 9 — the last kept digit is in the millions place
Next digit: 5 → round the 9 up, which carries: 149 → 150
Fill with zeros: 150,000,000 km
Unambiguous form: 1.50 × 10⁸ km
| Significant figures | Result |
|---|---|
| 1 | 100,000,000 (1 × 10⁸) |
| 2 | 150,000,000 (1.5 × 10⁸) |
| 3 | 1.50 × 10⁸ |
| 4 | 149,600,000 (1.496 × 10⁸) |
| 6 | 149,598,000 (1.49598 × 10⁸) |
Keeping trailing zeros meaningful
A rounded result often ends in zeros, and their meaning depends on how you write them:
- Zeros after a decimal point are significant. 2.5 rounded to 4 significant figures is 2.500, and those zeros must be written.
- Zeros ending a whole number look like placeholders. When some of them are significant, switch to scientific notation (1.50 × 10⁸) or, if the last significant digit is in the ones place, add a decimal point (100.).
- Carries can add a digit. 9.996 to 3 significant figures becomes 10.0, and 99.96 becomes 100. — the count of significant figures stays 3 even though the leading digit moved.
When to round to significant figures
- After multiplying or dividing measurements. The answer keeps as many significant figures as the least precise input. The significant figures calculator applies this rule automatically.
- When reporting physical constants or large data. A figure such as 8,118,835,999 is usually quoted as 8.12 billion.
- When comparing values of very different sizes — a fixed decimal-place rule would keep useless digits on large numbers and erase small ones entirely.
Need a fixed place instead, such as the nearest hundredth? Use the rounding calculator. To check how many significant figures a value already has, try the significant figures counter.
Frequently asked questions
How do you round a number to significant figures?
Start at the first non-zero digit and count the number of significant figures you want. Look at the next digit: if it is 5 or more, round the last kept digit up; otherwise leave it. Replace dropped digits to the left of the decimal point with zeros and drop those to the right.
What is 0.0045678 rounded to 2 significant figures?
0.0046. The first significant digit is the 4, the second is the 5, and the next digit, 6, rounds the 5 up to 6. The leading zeros stay as placeholders.
Why does my rounded answer show scientific notation?
When rounding leaves zeros at the end of a whole number, they look like placeholders. 149,597,870.7 rounded to 3 significant figures is 150,000,000, which a reader would count as 2. Writing 1.50 × 10⁸ shows all three clearly.
What is 99.96 rounded to 3 significant figures?
100. — with a decimal point. Rounding carries all the way up, and the trailing decimal point shows that both zeros are significant. In scientific notation it is 1.00 × 10².
Is rounding to significant figures the same as rounding to decimal places?
No. Decimal places count from the decimal point, so they ignore how large the number is. Significant figures count from the first non-zero digit, so 0.004567 and 4,567 both round to 3 significant figures as 0.00457 and 4,570.