Significant Figures — Rules Infographic & Examples

What's in this visual

Significant figures look simple and quietly cost marks all year — counting rules, two different arithmetic conventions and a rounding rule with an awkward exception. The infographic above gathers every rule into one place, with worked examples, so it works as a cheat sheet rather than a chapter to re-read. Here is the full breakdown.

What significant figures are

Every experimental measurement carries some uncertainty, set by the instrument used — a ruler marked in millimetres cannot honestly report a thousandth of a millimetre. Significant figures are how scientists express this honestly: they are the meaningful digits of a value, made up of all the digits known with certainty plus one final digit that is estimated. The number of significant figures therefore communicates the precision of the measurement. Getting this right is not pedantry — it is what stops a calculated answer from claiming more accuracy than the original data can support.

The rules for counting significant figures

Six rules decide how many significant figures a number has. All non-zero digits count — 285 has three. Zeros between non-zero digits count — 2.005 has four. Leading zeros do not count; they only place the decimal point, so 0.0052 has two. Trailing zeros after a decimal point do count — 0.200 has three. Trailing zeros with no decimal point generally do not — 100 has one, but 100. has three and 100.0 has four. And changing units changes nothing: 2.308 cm, 0.02308 m and 23.08 mm all have exactly four.

Scientific notation and exact numbers

Two ideas remove the ambiguity around zeros. Scientific notation writes a value in the form a × 10 to a power: every digit in the base number is significant and the power of ten is ignored, so 4.01 × 10² unambiguously has three significant figures. Exact numbers are the other special case — quantities that are counted (2 balls, 20 eggs) or exact mathematical factors, like the 2 in 2πr. These have an infinite number of significant figures and never limit the precision of a calculation, because they carry no uncertainty at all.

Rules for multiplication, division, addition and subtraction

Arithmetic uses two different rules, and mixing them up is the classic mistake. For multiplication and division, the result keeps the same number of significant figures as the input with the fewest — 2.5 × 1.25 = 3.125, but since 2.5 has only two, the answer is 3.1. For addition and subtraction, the result keeps the same number of decimal places as the input with the fewest — 436.32 + 227.2 + 0.301 = 663.821, but 227.2 has one decimal place, so the answer is 663.8. In multi-step calculations, keep one extra digit through the working and round only at the very end.

The rounding-off rules

Once you know how many significant figures to keep, three rules say how to round. If the digit being removed is greater than 5, increase the preceding digit by one — 1.386 to three figures becomes 1.39. If it is less than 5, leave the preceding digit unchanged — 4.334 becomes 4.33. The tricky case is when the removed digit is exactly 5: leave the preceding digit alone if it is even, but round it up if it is odd. So 6.25 becomes 6.2, while 6.35 becomes 6.4 — the 'round half to even' convention that keeps rounding unbiased.

Why a rules-heavy topic needs a cheat-sheet visual

Significant figures are not hard to understand once, but they are hard to recall correctly under exam pressure — which zeros count, which arithmetic rule applies, what to do with an exact 5. Read as prose, the rules sit in separate paragraphs and blur together. An infographic puts every rule and a worked example in one frame, so it works the way you actually use it: a glance next to your calculator, not a chapter to re-read mid-problem.

Frequently asked questions