Significant Figures Counter
Count the significant figures of any number and see for every digit why it counts or not, round to any number of significant figures with the steps shown, and write the number in scientific, E and engineering notation.
The Rules for Significant Figures
The significant figures of a measured value are the digits that carry information about its size: all the digits you are sure of, plus the last, estimated one. A ruler with millimetre marks gives 12.3 cm (3 significant figures); writing 12.30 cm would claim a precision the ruler does not have.
To make the zeros of 1200 count, write it in scientific notation (1.200 × 10³ has 4 significant figures, 1.2 × 10³ has 2) or put a decimal point after it: 1200. has 4. Exact numbers, such as counted objects (12 eggs) or defined values (1 inch = 2.54 cm), have unlimited significant figures.
Rounding: keep the wanted number of digits and look at the next one. If it is 5 or more, round the last kept digit up; otherwise leave it. This calculator rounds a 5 away from zero (2.5 → 3), as taught in most schools; some standards round an exact 5 to the even digit (2.5 → 2) instead.
Digit by Digit
digitsStep-by-Step Solution
Worked Techniques
Skip the leading zeros, then count every digit to the end: the zero between 4 and 5 and the final zero after the decimal point both count.
Keep three digits; the next digit is 1 (less than 5), so the 4 stays. For 0.0995 to 2 significant figures the 5 carries all the way: 0.0995 → 0.10.
Write only the significant figures in front of the power of ten: the number of digits then shows the precision without any doubt.
Sources & Verification
- J. R. Taylor, An Introduction to Error Analysis, 2nd ed., University Science Books, 1997 — Ch. 2 (how to state uncertainties and significant figures).
- A. Thompson & B. N. Taylor, Guide for the Use of the International System of Units (SI), NIST Special Publication 811, 2008 — Appendix B (rounding numbers).
Frequently Asked Questions
Why do significant figures matter at all?
Almost every measured value is a number we never know exactly. Take the temperature outside: right now it might really be 0.292819410123… °C, with digits that go on and on. Nobody knows all of them, and nobody needs to.
A normal thermometer gives us the nearest degree, or at best the nearest tenth: “0 °C” or “0.3 °C”. That is what we tell each other, and for daily life it is plenty: whether it is 0.29 or 0.3 degrees makes no difference to how cold it feels or which coat you wear.
Sometimes, though, that last digit is exactly what matters. At +0.2 °C ice slowly melts; at −0.2 °C water freezes. Rounded to whole degrees, both are simply “0 °C”, or “32 °F” in Fahrenheit (32.36 °F and 31.64 °F). Read to a tenth of a degree, the difference appears: 0.2 °C against −0.2 °C, or 32.4 °F against 31.6 °F.
Significant figures are how a number tells you how precisely it was measured. “0 °C” means “somewhere around freezing”; “0.2 °C” means “just above freezing”. The more precise the measurement, the more you can do with it, and a calculation can never be more precise than the measurements it starts from.
How do you count significant figures?
Start at the first nonzero digit and count every digit after it, with one exception: trailing zeros of a whole number without a decimal point. Example: 0.004050.
1. The leading zeros 0.00 only show where the decimal point is: not significant.
2. 4 and 5 are nonzero: significant.
3. The 0 between 4 and 5 is significant.
4. The final 0 comes after the decimal point, so it was measured: significant.
So 0.004050 has 4 significant figures, and in scientific notation it is 4.050 × 10⁻³.
Are trailing zeros significant?
After a decimal point, yes: 4.50 has 3 significant figures and 1200. (with a point) has 4. In a whole number without a decimal point they are ambiguous: 1200 could be measured to the nearest hundred or to the nearest unit, so it is counted as 2 significant figures (2 to 4). Scientific notation removes the doubt: 1.2 × 10³ has 2, 1.200 × 10³ has 4.
How do you round to significant figures?
Keep the wanted number of digits, counted from the first nonzero digit, and look at the next digit: 5 or more rounds the last kept digit up, less than 5 leaves it. 3.14159 to 3 significant figures is 3.14 (the next digit is 1). A 9 can carry: 0.0995 to 2 significant figures is 0.10. This calculator rounds an exact 5 away from zero (2.5 → 3), as taught in most schools; some standards round it to the even digit instead (2.5 → 2).
How many significant figures does a number in scientific notation have?
Count only the digits in front of the power of ten; the power just moves the decimal point. 6.022 × 10²³ has 4 significant figures, and so does 4.050 × 10⁻³. That is why scientific notation is the clearest way to show the precision of a very large or very small number.
Do exact numbers have significant figures?
Exact numbers have unlimited significant figures: counted objects (12 eggs, 3 trials) and defined values (1 inch = 2.54 cm, 100 cm in a metre) carry no measurement uncertainty, so they never limit the significant figures of a calculation. On the Calculate tab you can mark whole numbers as exact.