Converting a measurement cannot add information to it. A distance given as 10 miles is precise to about a mile, so its conversion is 16 kilometres — not 16.09344, which asserts a precision of a centimetre that nothing in the original supports. The conversion factor being exact is what misleads: an exact factor preserves whatever precision went in, and preserving two significant figures means producing two.
This is the most common way a correct calculation produces a wrong-looking answer, and converters make it easy because they have no way of knowing how precisely you measured.
How many digits is a conversion allowed to keep?
As many as the measurement had, and no more. The rule for multiplication is that the result carries the same number of significant figures as the least precise input, and a unit conversion is a multiplication.
| As given | Significant figures | Honest conversion |
|---|---|---|
| 10 miles | 2 | 16 km |
| 10.0 miles | 3 | 16.1 km |
| 10.00 miles | 4 | 16.09 km |
| 26.2 miles | 3 | 42.2 km |
| 26.219 miles | 5 | 42.195 km |
The last two rows are the marathon, and they show why the distinction is not academic. The distance is defined as 42.195 kilometres exactly, so the imperial figure is the derived one — and 26.2 miles is a rounding of it that cannot be converted back to the original without the digits reappearing from nowhere.
Which factors are exact, and does it matter?
More than people expect are exact by definition, and it matters less than people expect. An inch is exactly 25.4 millimetres, a pound is exactly 0.45359237 kilograms, and a mile follows from the inch. These are definitions rather than measurements, so they contribute no uncertainty at all.
That is precisely why the output precision is set by the input. If the factor were uncertain it would limit the answer too; because it is exact, the measurement is the only thing limiting it, and a two-figure measurement gives a two-figure answer however many digits the factor carries.
A genuinely measured factor behaves differently, and they do still exist — an ounce of gold against a gram is exact, but a barrel of oil against a litre depends on which barrel is meant. Where a factor is a convention rather than a definition, it is worth knowing which convention.
Why does temperature behave differently?
Because Celsius and Fahrenheit have different zero points, so the conversion is an offset as well as a scale. The significant-figure rule is written for multiplication and does not transfer cleanly to addition, where what matters is decimal places rather than significant digits.
In practice, a temperature given to the nearest degree converts to the nearest degree. 20 °C is 68 °F, not 68.0 °F, and the fact that the arithmetic produced a whole number is a coincidence rather than a measurement.
There is a second trap in temperature differences. A change of 10 °C is a change of 18 °F, not 50 °F, because an interval takes only the scale factor and not the offset. Converting a difference as though it were a point is a distinct error from the precision one and considerably more damaging.
Why do converters show so many digits, then?
Because the honest answer depends on something the tool was not told. A converter is given a number, not a measurement, and it cannot distinguish a rough 10 from a carefully determined 10.000 — so it shows the arithmetic and leaves the judgement to whoever supplied the input.
The right response is to round the output to the precision of your input rather than to expect the tool to guess it. Where a figure is going into a specification, that rounding is part of the work and not a cosmetic step.
Where does false precision cause real trouble?
In specifications, where a converted tolerance becomes a tighter tolerance than anyone intended. A part specified to the nearest millimetre converts to 0.03937 inches, and a workshop reading five decimal places may cost real money meeting a precision the drawing never asked for.
In reported data, where converted figures acquire authority they have not earned. A survey answer of about 5 kilometres becomes 3.106856 miles, and it reads like a measurement rather than the estimate it is.
In recipes and dosing, where the conversion is frequently the smaller error anyway. The cups-to-grams problem is that the input itself is not a fixed quantity, which no amount of decimal places in the conversion will repair.
Questions people ask
Do trailing zeros count? After a decimal point, yes — 16.10 claims the hundredths place was determined. Before one, 1500 is ambiguous, which is the problem scientific notation exists to solve by writing the digits you mean and the magnitude separately.
Should I round at each step of a chain? No. Carry the extra digits through the intermediate steps and round once at the end, or the rounding error compounds.
Is it ever right to show more digits than the measurement has? As an intermediate value that something else will consume, yes. As a final answer presented to a reader, it is a claim about the instrument, and it should be true.
What about currency conversion? The rate is a measurement of a moving thing, so it limits the answer as much as the amount does. Six decimal places on a converted price implies a rate that was exact to six places at a specific instant.
The conversion is the easy half; deciding how much of the answer to keep is the half that carries the meaning. The significant figures calculator shows how many digits a value is actually claiming, the scientific notation converter writes that claim unambiguously, and the rounding calculator applies the rule you have chosen.