Type 3 inches into any converter and it will offer you 76.2 millimetres. That answer is arithmetically correct and, as a statement about a real object, probably overstates what you know by a factor of ten.
A conversion moves information between units. It cannot create any. This guide is about carrying that idea through a calculation and reporting a result honestly.
Significant figures in one page
The significant figures in a number are the digits that carry real information about the measurement:
- All non-zero digits count.
247has three. - Zeros between non-zero digits count.
2.07has three. - Leading zeros never count.
0.0034has two. -
Trailing zeros after a decimal point count.
2.50has three — writing that final zero is a claim about precision. -
Trailing zeros in a whole number are ambiguous.
1500could be two, three or four. Scientific notation removes the doubt: 1.5 × 10³ is two, 1.500 × 10³ is four.
The two rules that matter
Multiplication and division — the result carries as many significant figures as the least precise input. Converting 3 in (one significant figure) by 25.4 gives 76.2, but you should report 80 mm, because "3 inches" claimed only one figure of precision.
Addition and subtraction — the result carries as many decimal places as the input with the fewest. 12.4 + 0.257 = 12.657, reported as 12.7, because the first number was only known to a tenth.
Exact factors are exempt. 25.4 mm per inch is a definition, not a measurement, so it has unlimited significant figures and never limits your result. The same goes for 2.54, 0.3048, 0.45359237, 12 inches per foot and 1,000 metres per kilometre. Only measured quantities constrain precision.
Worked examples
A measured length
A board measures 3 ft 6 in on a tape marked in sixteenths. The tape resolves to about 1/16 in, so the measurement is 42 in ± 0.03 in — roughly four significant figures. Converting: 42 × 25.4 = 1066.8 mm. Reporting 1067 mm is honest. Reporting 1066.80 mm is not, and reporting 1000 mm throws away information you had.
A rounded input
A recipe says "about 2 cups". That is one significant figure at best. 2 × 236.5882365 = 473.1764730 mL, of which the only defensible answer is "about 500 mL", or 473 mL if you intend to measure it precisely and want the exact equivalent of two cups.
A temperature
20 °C measured to the nearest degree becomes 68 °F — but the true value lies somewhere in 19.5–20.5 °C, which is 67.1–68.9 °F. The Fahrenheit figure looks more precise because its degrees are smaller. It is not. This is the general trap of converting into a finer unit.
Rounding early is the expensive mistake
Convert 1.75 m to feet and inches:
| Approach | Working | Result |
|---|---|---|
| Round at each step | 1.75 × 3.28 = 5.74 ft → 0.74 × 12 = 8.9 in | 5 ft 8.9 in |
| Round once at the end | 1.75 × 3.280839895 = 5.74147 ft → 0.74147 × 12 = 8.898 in | 5 ft 8.9 in |
Here they agree, because the conversion is short. Now do it fifty times in a cut list, or chain four conversions together in a unit-heavy engineering calculation, and the intermediate roundings accumulate. The rule is simple and universal: carry full precision through the working, round once at the end. This is why UnitFlip computes at full double precision and rounds only the displayed value.
Which rounding rule?
The tie case — exactly half — has more than one convention, and they give different answers:
| Rule | 2.5 → | 3.5 → | Where used |
|---|---|---|---|
| Half up | 3 | 4 | Everyday arithmetic, most calculators |
| Half to even ("banker's") | 2 | 4 | Statistics, finance, IEEE 754 |
| Half away from zero | 3 | 4 | Many programming languages' round() |
Half-to-even exists because always rounding halves upward biases a long series of numbers upward. Over a large dataset that bias is measurable. For a single conversion it makes no practical difference — but if you are summing thousands of rounded values, it does.
Floating point: a separate source of noise
Computers store most decimal fractions in binary approximations. The
classic demonstration is that 0.1 + 0.2 evaluates to
0.30000000000000004 in virtually every language, because neither 0.1 nor 0.2
has an exact binary representation.
Conversions inherit this. Multiplying by 2.54 and dividing back does not always return the original number's exact bits. The error is around 10⁻¹⁶ relative — nowhere near any physical measurement's precision — but it shows up as trailing garbage digits if a program prints full precision. Formatting the result to a sensible number of figures is what removes it, which is one more reason to round for display rather than to trust every digit a calculator hands you.
How many figures should you report?
| Context | Suggested precision |
|---|---|
| Everyday conversation | 2 significant figures |
| Cooking | Nearest 5 g or 5 mL |
| Body weight and height | Nearest 0.1 kg, nearest cm or inch |
| Construction | Nearest mm or 1/16 in |
| Machining | 0.01 mm or 0.001 in, per the drawing tolerance |
| Laboratory work | Whatever the instrument resolves, no more |
The three rules to keep
- A conversion never adds precision. The answer is only as good as the measurement.
- Definitional factors are exact and never limit the result.
- Carry full precision through the working; round once, at the end, for the reader.
For how these rules are applied to the numbers this site produces, see the methodology page.