Significant Figures
Type a number, including scientific notation like 1.20e-3
Follows the standard significant-figure rules used in chemistry. Read the rules →
The Significant Figure Rules
- All non-zero digits are significant.
- Zeros between non-zero digits are significant (e.g. 1002 has 4).
- Leading zeros are never significant (0.0045 has 2).
- Trailing zeros are significant only if a decimal point is shown (1500 has 2; 1500. or 1.500×10³ has 4).
- In scientific notation, every digit in the mantissa counts.
When multiplying or dividing, the answer keeps the fewest significant figures of the inputs. When adding or subtracting, keep the fewest decimal places. More detail in the significant figures guide.
Worked Example — Applying Sig-Fig Rules to a Calculation
Question: A burette reading of 12.50 mL is added to a separate volume of 3.0 mL. Then, a concentration of 4.20 M is multiplied by a volume of 3.1 L. Report both results to the correct number of significant figures.
Addition (12.50 + 3.0): for addition/subtraction, the result is limited by the fewest decimal places among the inputs. 12.50 has 2 decimal places, 3.0 has 1 — so the answer is rounded to 1 decimal place.
12.50 + 3.0 = 15.50 → reported as 15.5
Multiplication (4.20 × 3.1): for multiplication/division, the result is limited by the fewest significant figures among the inputs. 4.20 has 3 sig figs, 3.1 has 2 — so the answer is rounded to 2 sig figs.
4.20 × 3.1 = 13.02 → reported as 13
Answer: 15.5 mL and 13 (the units would depend on what 4.20 M × 3.1 L represents, e.g. mol).
Common Mistakes
- Using one rule for everything. Addition/subtraction is governed by decimal places; multiplication/division is governed by significant figures. A calculation mixing both operations needs the rule applied at each step, not just at the end.
- Rounding intermediate steps. Round only the final answer of a multi-step calculation — rounding partway through introduces small errors that can accumulate.
- Treating exact numbers as measurements. Defined conversion factors (1000 mL = 1 L) and counted quantities (3 flasks) have effectively infinite significant figures and never limit the result.
Frequently Asked Questions
All non-zero digits are significant. Zeros between non-zero digits are significant. Leading zeros are never significant. Trailing zeros are significant only if there is a decimal point. In scientific notation, every digit in the mantissa is significant.
Only when a decimal point is shown. 1500 has 2 significant figures (the trailing zeros are ambiguous), but 1500. or 1.500×10³ has 4.
No. Defined relationships (1000 mL = 1 L, 1 m = 100 cm) and counted whole numbers (2 moles of a reactant from a balanced equation) are exact — they have effectively infinite significant figures and never limit the precision of a result. Only measured quantities (a mass read from a balance, a volume read from a burette) limit significant figures.
Match the precision of your least-precise measured input: for multiplication and division, count significant figures and use the smallest count; for addition and subtraction, count decimal places and use the smallest count. If a calculation mixes both, apply the relevant rule at each step rather than only at the very end.