What are significant figures?
Significant figures (or "sig figs") are the digits in a number that carry real, measured meaning about its precision. They include every certain digit plus one estimated final digit. For example, the measurement 3.0857 has five significant figures, while 0.0085 has only two because the leading zeros are just placeholders. Significant figures matter in science, engineering, and chemistry because they tell you how precise a measurement is and prevent you from reporting more accuracy than your instruments actually provide.
How do you count significant figures?
To count the significant figures in a number, apply a short set of rules in order. Start from the first non-zero digit on the left and count every digit until the last meaningful one. This calculator does it automatically — enter any number and it reports the exact count. For instance, 20007 has five significant figures and 2.500 has four. If you also work with averages and spreads, pair this with our mean, median, and mode calculator.
What are the rules for significant figures?
Five rules cover almost every case:
- All non-zero digits are significant. 211.8 has four sig figs.
- Zeros between non-zero digits are significant. 20,007 has five sig figs.
- Leading zeros are never significant. 0.0085 has two sig figs.
- Trailing zeros after a decimal point are significant. 2.500 has four sig figs.
- Trailing zeros in a whole number with no decimal point are not significant. 320 has two sig figs, but 320. has three.
How do you round to significant figures?
To round a number to n significant figures, keep the first n significant digits and round the last one using the standard rule: if the next digit is 5 or more, round up; otherwise round down. Any digits to the left of the decimal that you drop are replaced with zeros to preserve the number's magnitude. For example, 356 rounded to two significant figures is 360, and 3.0857 rounded to three sig figs is 3.09. This is different from rounding to decimal places — see our percentage calculator for related rounding in everyday math.
What is the difference between significant figures and decimal places?
Significant figures count meaningful digits from the first non-zero digit, regardless of where the decimal point sits. Decimal places count only the digits after the decimal point. The number 0.00420 has three significant figures but five decimal places. Scientists prefer significant figures because they describe relative precision, while decimal places describe absolute position. This calculator reports both so you can compare them directly.
How do significant figures work in scientific notation?
Scientific notation makes significant figures unambiguous. A number written as 1.2 × 10³ clearly has two significant figures, whereas the plain form 1200 is ambiguous. To write a number in scientific notation, move the decimal point so one non-zero digit sits in front of it, keep exactly the significant digits in the mantissa, and record the shift as a power of ten. This calculator shows the scientific-notation form of your rounded result automatically.
Why are significant figures important?
Significant figures stop you from overstating precision. If you measure a length as 4.2 cm with a ruler, reporting 4.2000 cm falsely implies your ruler resolves ten-thousandths of a centimetre. In multiplication and division, the result should carry the same number of significant figures as the least precise input; in addition and subtraction, the result is limited to the least precise decimal place. Using sig figs correctly keeps calculated results honest about their underlying uncertainty. For more advanced math, try our scientific calculator.