How Precise Should a Unit Conversion Be? Significant Figures Made Simple
Type “6 ft” into a converter and you get 1.8288 m. That answer is mathematically exact, because the foot has been defined as exactly 0.3048 m since 1959. But if the 6 ft was someone’s height estimated by eye, writing it as 1.8288 m claims a precision to a tenth of a millimetre that never existed.
Converting a number correctly is only half the job. The other half is deciding how many digits the answer deserves. This guide explains the idea of significant figures, gives practical rounding rules, and shows why getting units right really matters.
Exact definitions vs measured values
Some conversion factors are exact by definition. Since the international yard and pound agreement of 1959:
- 1 inch = 25.4 mm exactly
- 1 foot = 0.3048 m exactly
- 1 pound = 0.45359237 kg exactly
Others are defined in terms of other units and are also exact, such as 1 US gallon = 231 cubic inches. And some factors are measured or conventional, like the weight of a cup of flour, which depends on how it was packed.
But the factor is rarely the weak link. The weak link is usually the value you start with. A measurement is only as precise as the tool and the person who made it, and no conversion can add precision that wasn’t there.
What significant figures are
Significant figures are the digits in a number that carry real information:
| Value | Significant figures | Meaning |
|---|---|---|
| 6 ft | 1 | “about six feet” |
| 6.0 ft | 2 | measured to the nearest tenth of a foot |
| 6.00 ft | 3 | measured to the nearest hundredth |
| 0.0045 m | 2 | leading zeros only set the decimal point |
| 1,200 m | 2 to 4 | ambiguous; scientific notation removes doubt |
The basic rule for multiplying or dividing, which is what most unit conversions are, is this:
Round the result to the same number of significant figures as the least precise input.
Exact conversion factors don’t count, because they have unlimited precision. So:
- 6 ft (1 significant figure) → 1.8288 m → about 2 m
- 6.0 ft (2) → 1.8 m
- 6.00 ft (3) → 1.83 m
In everyday use you don’t need to be that strict, but the principle holds: your answer should not look more precise than your question.
Practical rounding guidelines
| Situation | Sensible precision |
|---|---|
| Weather, body temperature | Whole degrees, or one decimal for fever |
| Height, distance in conversation | 2–3 significant figures (1.83 m, 42 km) |
| Cooking | Whole grams, or the nearest 5 g |
| Road distances | Whole kilometres or miles |
| DIY and woodworking | Nearest millimetre or 1/16 inch |
| Engineering drawings | As specified on the drawing, with tolerances |
| Scientific data | Keep all digits during calculation, round only the final result |
That last rule is important: round once, at the end. If you convert, round, convert again and round again, the small errors add up. For example, converting 1 mile to km and rounding to 1.6 km, then back to miles, gives 0.994 mi — a 0.6 % error from just two steps.
Rounding and computers
Calculators and converters work with binary floating-point numbers, which cannot represent some decimal fractions exactly. That’s why some programs show 0.1 + 0.2 as 0.30000000000000004. Converters like EveryUnit calculate with about 15–17 significant digits and then format the result for display, so these tiny errors never show up in normal use.
On EveryUnit you can choose how results are displayed under Output Number Format: a fixed number of decimal places, a number of significant figures, or scientific notation for very large and very small values. Pick the format that matches how precise your input really is.
When units go wrong: two famous examples
Precision is about how many digits to keep. Getting the unit wrong is a far bigger problem, and history has some expensive examples.
Mars Climate Orbiter (1999). NASA lost a 125-million-dollar spacecraft because one team’s software reported thruster impulse in pound-force seconds while the navigation team expected newton-seconds. The difference, a factor of about 4.45, gradually pushed the spacecraft off course until it entered the Martian atmosphere far too low and was destroyed.
The “Gimli Glider” (1983). An Air Canada Boeing 767 ran out of fuel in mid-flight because the fuel load had been calculated using pounds instead of kilograms during the airline’s switch to metric. The aircraft carried less than half the fuel the crew believed. The pilots glided it to a safe landing at a former air force base in Gimli, Manitoba.
Both accidents happened to professional teams with careful procedures. The lesson for everyone else is to always label your numbers with their units, and to double-check any conversion that something important depends on.
A checklist for reliable conversions
- Write the unit next to every number, including intermediate results.
- Check which variant of a unit you have: US or imperial gallons, short or long tons, US or metric cups.
- Keep full precision during calculations and round only the final answer.
- Round to the precision of your input, not to the number of digits the calculator shows.
- Sanity-check the result. A person 18 m tall or a car using 0.5 L/100 km means something went wrong.
- For safety-critical, medical, legal or financial work, verify against an official source. A general-purpose converter is a convenience, not a certified instrument.
Key takeaways
- Most modern conversion factors are exact; the precision of the result is limited by your input value.
- Round the result to the number of significant figures of your least precise measurement.
- Round once, at the end, never between steps.
- Always label numbers with units; most real-world conversion disasters are unit mix-ups, not rounding errors.
You can adjust decimal places, significant figures and notation for any conversion on EveryUnit, starting from the home page converter.