What significant figures communicate
Significant figures are the digits used to communicate the precision of a measured value. The measurements 2.4 m and 2.400 m have the same approximate size, but the second records finer resolution. A calculator may display many more digits after conversion; those digits do not automatically represent additional knowledge about the original measurement.
Significant figures are not the same as decimal places. The value 0.00420 has five decimal places but three significant figures. The value 1,250.0 has one decimal place and five significant figures. Scientific notation is often the clearest way to show intent: 1.2 × 10³, 1.20 × 10³, and 1.200 × 10³ state different precision.
How to count them
Begin at the first nonzero digit, then count meaningful digits to the end of the stated measurement. The treatment of zeros depends on their position, so context and notation matter.
- Every nonzero digit is significant: 27.4 has three significant figures.
- Zeros between nonzero digits are significant: 1.005 has four.
- Leading zeros only locate the decimal point: 0.0042 has two.
- Trailing zeros to the right of a decimal are significant: 12.00 has four.
- Trailing zeros in a whole number may be ambiguous: write 1.20 × 10³ to state three significant figures.
Exact values do not consume precision
A defined conversion such as 1 in = exactly 2.54 cm has no conversion uncertainty for this purpose. Counted quantities can also be exact: 12 objects is an exact count when every object is included. These exact numbers do not limit the significant figures of a calculated result.
Measured inputs are different. If a board is recorded as 36 in to the nearest inch, converting with the exact inch definition produces 91.44 cm on a calculator, but reporting every digit would imply more resolution than the measurement supports. The appropriate rounding depends on how the input was measured and how the result will be used—not simply on the converter’s display.
Round once, at the end
Carry guard digits through intermediate calculations and round the final value once. Repeated rounding can shift a result. When multiplying or dividing ordinary measured values, the least-precise input is a useful introductory guide, but a stated uncertainty or tolerance is better evidence when one is available.
To round, inspect the first digit you will discard. If it is below 5, leave the retained digit unchanged; if it is above 5, increase the retained digit by one. Exact halfway cases require a declared rule. NIST conversion tables use round-to-even in the examples they describe, which avoids a consistent upward bias across many values.
- Keep the original measurement and unit in your notes.
- Use scientific notation when trailing zeros would be unclear.
- Do not add decimal places merely because the conversion factor is exact.
- For regulated work, use the required uncertainty and rounding procedure rather than a general shortcut.
Worked conversion example
Suppose a distance is measured as 7.25 mi, with three significant figures. The exact international conversion gives 7.25 × 1.609344 = 11.667744 km. A sensible reported result is 11.7 km, while the unrounded value can be retained internally for a later calculation.
If the input were 7.250 mi, the extra trailing zero communicates finer precision and 11.67 km may be appropriate. The unit conversion is identical; only the evidence carried by the measured input has changed.
Put this guide into practice
Enter the same value with different stated precision and compare the full calculator output with the value you would responsibly report.
- Miles to kilometres: Practise rounding an exact length conversion.
- Pounds to kilograms: Compare display precision with a measured input.
- Celsius to Fahrenheit: See why an exact formula still cannot improve a thermometer reading.
Sources and standards
The definitions and factors in this guide were checked against these primary standards and government references.