How to Calculate with Significant Figures

Significant figures (or "sig figs") communicate the precision of a measurement. A measurement of 3.50 cm is more precise than 3.5 cmβ€”the trailing zero tells us the measurement was made to the nearest hundredth of a centimeter.

Rules for Counting Significant Figures

  1. All non-zero digits are significant: 4,832 has 4 sig figs
  2. Zeros between non-zeros are significant: 1,007 has 4 sig figs
  3. Leading zeros are NOT significant: 0.0042 has 2 sig figs
  4. Trailing zeros after a decimal point ARE significant: 3.50 has 3 sig figs
  5. Trailing zeros in a whole number are ambiguous (use scientific notation to clarify)

Significant Figures in Calculations

Multiplication and Division

Round your answer to the same number of sig figs as the measurement with the fewest sig figs.

Example: 4.52 Γ— 1.4 = 6.328 β†’ 6.3 (2 sig figs, limited by 1.4)

Addition and Subtraction

Round your answer to the same number of decimal places as the measurement with the fewest decimal places.

Example: 12.11 + 0.3 = 12.41 β†’ 12.4 (1 decimal place, limited by 0.3)

Step-by-Step Example

Calculate the area of a rectangle with measurements 6.4 cm Γ— 12.35 cm.

6.4 Γ— 12.35 = 79.04 cmΒ²

6.4 has 2 sig figs; 12.35 has 4 sig figs β†’ Round to 2 sig figs: Area = 79 cmΒ²

Scientific Notation and Sig Figs

Scientific notation removes ambiguity:

  • 3,400 (ambiguous) vs. 3.4 Γ— 10Β³ (2 sig figs) vs. 3.40 Γ— 10Β³ (3 sig figs)

Use our significant figures calculator to count sig figs or round any result.