MathIsimple
Sig Fig Rules

Significant Figures Rules

Every sig-fig rule with examples — plus a live counter that tells you how many significant figures a number has and exactly which rule applies.

All 5 Rules with ExamplesLive Sig-Fig CounterRounding & Operation Rules
Count Significant Figures
Type any number — decimals, whole numbers, or scientific notation like 4.56e-3

The Rules at a Glance

RuleExampleSig figs
Nonzero digits always count4.563
Sandwiched zeros count4,0564
Leading zeros never count0.004563
Trailing zeros count with a decimal point45.604
Trailing zeros without a decimal are ambiguous4,5603 (assumed)
Scientific notation: all mantissa digits4.560 × 10³4

Why the Rules Exist: Precision Is a Claim

Significant figures encode how precisely something was measured. Reporting 45.60 mL claims your glassware resolves hundredths of a milliliter; reporting 45.6 mL claims only tenths. That's why leading zeros never count (0.00456 kg is the same measurement as 4.56 g — repackaging units can't add precision) and why trailing zeros do count when a decimal point makes them deliberate. The operation rules follow the same logic: a chain of calculations can't be more precise than its least precise measurement — the weakest link caps the claim.

The Two Operation Rules, Worked

Addition/subtraction → fewest decimal places. 12.52 + 1.7 + 0.008 = 14.228 → 14.2, because 1.7 only claims tenths. Multiplication/division → fewest sig figs. A density from mass 4.56 g and volume 1.4 mL: 4.56 ÷ 1.4 = 3.2571… → 3.3 g/mL, two sig figs from the volume. Chained calculations: keep guard digits throughout and round once at the end — rounding at every step compounds error, which is exactly what our significant figures calculator automates. When you're ready, test yourself on the sig fig practice page.

Frequently Asked Questions

What are the 5 rules for significant figures?
1) Nonzero digits always count. 2) Zeros between nonzero digits count. 3) Leading zeros never count. 4) Trailing zeros count only if there's a decimal point. 5) In scientific notation, every mantissa digit counts. Examples: 4.56 → 3; 4,056 → 4; 0.00456 → 3; 45.60 → 4; 4,560 → 3 (ambiguous); 4.560×10³ → 4.
Are trailing zeros significant?
With a decimal point, yes: 45.60 has 4 sig figs — the zero asserts measurement precision to the hundredths. Without one, they're ambiguous: 4,560 could be 3 or 4 sig figs, and the convention is to count 3. Scientists write 4.560×10³ or 4.56×10³ precisely to remove that ambiguity.
What's the sig-fig rule for addition and subtraction?
Round to the fewest DECIMAL PLACES among the inputs, not the fewest sig figs: 12.52 + 1.7 = 14.22 → 14.2 (one decimal place, from 1.7). A number's total sig-fig count is irrelevant here — 1,000.1 + 0.02 = 1,000.1 despite the inputs having 5 and 1 sig figs.
What's the sig-fig rule for multiplication and division?
Round to the fewest SIG FIGS among the inputs: 4.56 × 1.4 = 6.384 → 6.4 (two sig figs, from 1.4). Mixing up the addition rule (decimal places) and multiplication rule (sig figs) is the most common exam error — the operations use different currencies of precision.
Do exact numbers limit sig figs?
No. Counted quantities (12 students), defined conversions (exactly 2.54 cm per inch), and integer multipliers have infinite sig figs and never limit a result. Converting 3.75 inches to cm keeps 3 sig figs: 3.75 × 2.54 = 9.525 → 9.53 cm — the 2.54 doesn't cap it.
How do I round 5s — is 2.5 rounded to 2 or 3?
Standard rounding says round half up: 2.5 → 3. Some chemistry courses teach 'round half to even' (banker's rounding): 2.5 → 2, 3.5 → 4, which cancels rounding bias over many measurements. Use whichever your course specifies — and state it when it matters.
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