How To Count Significant Figures Calculator
Significant figures are the digits in a number that carry real information. They exist because a measurement is only as precise as the instrument that produced it, and reporting extra digits implies a precision that was never measured.
Rounded value
12,300
- Order of magnitude
- 4
- Size of the rounding change
- 45
- Rounding position, negative means trailing zeros
- -2
Values update as you type. This calculator covers the single scenario its formula assumes — see Common Mistakes for what it leaves out.
The formula this calculator uses
rounded = round(x, sigFigs - 1 - floor(log10(|x|)))
- x
- The number you are rounding
- sigFigs
- How many significant digits to keep
- floor(log10(|x|))
- The order of magnitude, or power of ten
- rounded
- The result, carrying exactly sigFigs digits
How to check the result by hand
- 1
Identify the first non-zero digit
Leading zeros are placeholders and never count. In 0.0072151 the counting starts at the 7, so the number has seven significant figures.
- 2
Read off the order of magnitude
The base ten logarithm, rounded down, tells you the power of ten the number starts at. For 12,345 that is 4; for 0.0072151 it is -3.
- 3
Convert significant figures into decimal places
Subtract the order of magnitude from the significant figures and take one away. Twelve thousand three hundred and forty-five to three significant figures gives a rounding position of -2, meaning two trailing zeros.
- 4
Round, then check the digit count
Round 12,345 to the hundreds place to get 12,300. Count the digits from the first non-zero one to confirm three, and note that the trailing zeros need scientific notation to be unambiguous.
- 5
Carry the result forward without adding digits
Once rounded, the extra digits are gone for good. Re-deriving them by operating on the rounded number simply invents precision that the measurement never had.
For worked examples, common mistakes and the limits of this formula, read the full How To Count Significant Figures page.