Sig Fig Calculator

Four rules cover everything: (1) non-zero digits are always significant; (2) zeros between significant digits are significant (505 has three); (3) leading zeros are never significant — they only place the decimal (0.0045 has two); (4) trailing zeros are significant only if a decimal point is written (4.500 has four; 4500 is ambiguous, conventionally two). The digit-by-digit display applies these so you see which rule fired where.

Because the notation genuinely can't say whether those zeros were measured or are placeholders — 1200 measured to the nearest hundred has 2 sig figs; to the nearest unit, 4. Convention (and this tool) reads bare trailing zeros as not significant, but the honest fix is scientific notation, which forces the claim: 1.2 × 10³ says two, 1.200 × 10³ says four. Chemistry teachers deduct points for exactly this.

Two rules, commonly confused: multiplication and division keep the fewest sig figs of any input (2.5 × 3.42 → 8.6, two sig figs); addition and subtraction keep the fewest decimal places instead (12.52 + 1.7 → 14.2, one decimal). Round once at the end of a multi-step calculation, not at every step — intermediate rounding compounds error.

They're a claim about measurement quality: reporting 9.81 m/s² asserts you know the value to about ±0.005 — writing 9.8100 claims a hundred times more precision than a classroom experiment has. Carrying fake digits misleads anyone using your number. Sig figs are the compact convention for keeping stated precision honest, which is why science grading enforces them.