Significant figures and rounding: how precise should a conversion be?
Why 1 mile is not “1.609344000 km” on a road sign, how to choose sensible precision, and when exact factors matter.
A converter can give you twelve or more digits. Whether you should keep them depends on how precisely the original value was measured. Converting “about 5 miles” to 8.04672 km implies a precision the original never had.
The rule of thumb
Keep the same number of significant figures in the answer as the least precise input. Significant figures are the digits that carry meaning: in 0.00450 there are three (4, 5 and the trailing 0), because leading zeros only set the decimal point.
- A bathroom scale reads 72.4 kg (three significant figures) → 160 lb, not 159.6146778 lb.
- A machinist measures 12.700 mm (five figures) → 0.5 in.
Exact conversion factors do not limit precision
Defined factors such as 2.54 cm per inch or 0.45359237 kg per pound are exact; they have unlimited significant figures and never reduce the precision of your result. Only measured or approximate factors do — for example the speed of sound used for “Mach”, which changes with air temperature.
Round once, at the end
Rounding intermediate results compounds error. Converting 100 °F to Celsius and back with rounding at each step can drift by a tenth of a degree; doing the arithmetic at full precision and rounding only the final figure does not. Our converters calculate in double precision (about 15–17 significant digits) and only round for display.
Choosing a display format
The universal converter and every converter card offer four formats:
- Auto — up to 12 significant figures, trailing zeros removed, scientific notation for very large or small values.
- Significant figures — exactly the number of figures you choose, keeping trailing zeros (useful for lab reports).
- Fixed decimals — a set number of places after the decimal point (useful for money-like quantities and tolerances).
- Scientific — always in the form a × 10ⁿ.
Floating-point surprises
Computers store most decimals in binary, so 0.1 + 0.2 is internally 0.30000000000000004. A careful converter hides this by rounding to fewer digits than the hardware provides. If you ever see a result like 12.700000000000001 elsewhere, that is binary representation showing through — the true answer is 12.7.