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.
| Rule | Example | Sig figs |
|---|---|---|
| Nonzero digits always count | 4.56 | 3 |
| Sandwiched zeros count | 4,056 | 4 |
| Leading zeros never count | 0.00456 | 3 |
| Trailing zeros count with a decimal point | 45.60 | 4 |
| Trailing zeros without a decimal are ambiguous | 4,560 | 3 (assumed) |
| Scientific notation: all mantissa digits | 4.560 × 10³ | 4 |
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.
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.
Calculate complex expressions and apply significant figures rules automatically with step-by-step explanations.
18 significant-figures practice problems with instant feedback, explanations, and score tracking — counting, rounding, and operations.
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