Significant Figures Calculator
Identify significant figures in numbers, round to specified precision, and perform calculations with proper significant figure rules.
What are significant figures and why do they matter?
Significant figures (sig figs) indicate precision of a measurement. They include all certain digits plus one uncertain digit. Rules: All non-zero digits are significant (123 has 3). Zeros between non-zeros are significant (1005 has 4). Leading zeros are NOT significant (0.0025 has 2). Trailing zeros after decimal ARE significant (2.500 has 4). Matter in science/engineering to communicate measurement precision and prevent false accuracy in calculations.
How do I count significant figures?
Counting rules: 1) All non-zero digits count (456 = 3 sig figs). 2) Zeros between non-zeros count (4006 = 4). 3) Leading zeros DON'T count (0.00456 = 3). 4) Trailing zeros after decimal count (45.600 = 5). 5) Trailing zeros in whole numbers are ambiguous (4500 = 2, 3, or 4 depending on measurement). Use scientific notation for clarity: 4.5*10^3=2 sig figs, 4.50*10^3=3 sig figs.
What are the sig fig rules for multiplication and division?
Multiplication/Division: Result has same sig figs as measurement with FEWEST sig figs. Example: 4.56 (3 sig figs) * 1.4 (2 sig figs) = 6.384... → round to 6.4 (2 sig figs). Why: Your answer can't be more precise than your least precise measurement. 100.0 (4 sig figs) / 3.0 (2 sig figs) = 33.333... → 33 (2 sig figs). Always identify fewest sig figs first, then round final answer.
What are the sig fig rules for addition and subtraction?
Addition/Subtraction: Result has same DECIMAL PLACES as measurement with fewest decimal places (not fewest sig figs!). Example: 123.25 (2 decimals) + 46.4 (1 decimal) + 0.235 (3 decimals) = 169.885 → round to 169.9 (1 decimal, matching 46.4). Why: Precision limited by least precise place value. Note: 1000 (no decimals) + 0.0005 (4 decimals) = 1000 (no decimals shown).
How do I round to significant figures?
Rounding to N sig figs: 1) Count N digits from first non-zero digit. 2) Look at next digit. 3) If >=5, round up; if <5, round down. Example: Round 0.004562 to 2 sig figs: First non-zero is 4, count 2 (4,5), next is 6 → round up → 0.0046. Round 12,450 to 3 sig figs: Count 3 (1,2,4), next is 5 → round up → 12,500 (better: 1.25*10⁴). Use scientific notation to show trailing zeros clearly.