Significant Figures & Rounding
What significant figures are, the rules for counting them, and how to round correctly — especially when converting units.
Last updated: 2026-05-21
What Are Significant Figures?
Significant figures (sig figs) are the digits in a number that carry real, measured meaning. They tell a reader how precisely a value is known. A length recorded as 12.3 cm claims precision to a tenth of a centimeter; the same length written as 12.300 cm claims precision to a thousandth. Both describe the same physical quantity, but they make very different statements about the measurement.
Precision is not the same as accuracy. Accuracy is how close a value is to the true result; precision is how finely it is reported. Significant figures track precision, and they exist to keep you honest: a number should never imply more certainty than the instrument or source actually delivered.
The Counting Rules
Four rules cover almost every case. Apply them left to right across the digits.
| Rule | Example | Sig figs |
|---|---|---|
| All non-zero digits count | 34.78 | 4 |
| Zeros between non-zero digits count | 40.06 | 4 |
| Leading zeros never count | 0.00420 | 3 |
| Trailing zeros count only with a decimal point | 2.50 | 3 |
The last rule is the one people stumble on. In 2.50 the final zero counts, giving three significant figures. But a bare 250 is ambiguous — the trailing zero could be a measured digit or just a placeholder, so it may represent two or three sig figs. The clean fix is scientific notation: 2.5 × 102 shows two, while 2.50 × 102 shows three, with no guesswork.
Rounding Rules
Once you decide how many significant figures to keep, you round off the rest. Look at the first digit you are dropping. If it is less than 5, leave the last kept digit unchanged (round down). If it is greater than 5, increase the last kept digit by one (round up). So 3.14159 rounded to three sig figs is 3.14, and 2.7182 rounded to three sig figs is 2.72.
The tie case — a dropped digit of exactly 5 with nothing meaningful after it — has two accepted conventions. Round half up always bumps the last digit upward, so 2.45 becomes 2.5. This is the rule taught in most classrooms.
Round half to even, also called banker’s rounding, instead rounds toward the nearest even digit: 2.45 becomes 2.4, while 2.55 becomes 2.6. Because it pushes ties up half the time and down half the time, it removes the small upward bias that round-half-up introduces across large datasets. It is the default in many spreadsheets and programming languages, so know which one your tools use before reporting results.
Sig Figs in Conversions
Unit conversion is where false precision sneaks in most often. A calculator multiplies your value by a long conversion factor and hands back a dozen digits — but those digits are not all real. The rule for multiplication and division is simple: the result keeps as many significant figures as the least precise measurement you started with.
Defined conversion factors do not limit you. Relationships such as 1 mile = 1.609344 km or 1 inch = 2.54 cm are exact by definition, so they carry infinite significant figures. Only your measured values constrain the answer.
Worked example: convert 5.0 miles to kilometers. The value 5.0 has two significant figures. Multiply by the exact factor: 5.0 × 1.609344 = 8.04672 km. Now round to two sig figs to match the input, and the honest result is 8.0 km — not 8.04672 km. Reporting all five digits would claim a precision your original measurement never had.
The same logic runs in reverse and across every category. Convert 250.0 g (four sig figs) and you may keep four; convert a rough 250 g and you should report only two or three. When you run a value through our converters, treat the full-precision output as a starting point, then round it down to the significant figures your source data actually supports.
Quick Reference
- Non-zero digits: always significant.
- Captive zeros (between non-zeros): always significant.
- Leading zeros: never significant.
- Trailing zeros: significant only with a decimal point.
- Multiplication & division: keep the fewest sig figs of any input.
- Exact factors (2.54, 1.609344, 12): never limit precision.
Get comfortable with these rules and your conversions will report exactly the precision you earned — no more, no less. Ready to put them to work? Try them on all converters.