Complete Guide to Significant Figures (Sig Figs) Rules & Calculations

In experimental science, physics, and chemistry, every measurement contains an inherent degree of uncertainty. Significant figures (also called sig figs or significant digits) reflect the precision of the measuring instrument. Writing an answer with too many digits claims a false degree of accuracy, while too few discards valuable observational data.

The 5 Core Rules of Significant Digits

1. Non-Zero Digits: Any digit from 1 to 9 is always significant (e.g. 487 has 3 sig figs).
2. Captive Zeros (Sandwich Rule): Zeros between non-zero digits are always significant (e.g. 4007 has 4 sig figs; 1.08 has 3 sig figs).
3. Leading Zeros: Zeros before the first non-zero digit are place-holders and are never significant (e.g. 0.0025 has only 2 sig figs).
4. Trailing Zeros with Decimal: Zeros at the end of a number that contains a decimal point are always significant (e.g. 92.00 has 4 sig figs; 0.0500 has 3 sig figs).
5. Trailing Zeros without Decimal: Zeros at the end of a whole number without a decimal point are ambiguous (e.g. 1500 could have 2, 3, or 4 sig figs). To avoid ambiguity, use scientific notation (1.50 × 10³ for 3 sig figs) or a trailing decimal (1500. for 4 sig figs).

Arithmetic Rules: Multiplication vs. Addition

• Multiplication & Division: Count significant figures. The final answer has the same number of sig figs as the input with the smallest count.
• Addition & Subtraction: Count decimal places. The final answer has the same number of decimal places as the input with the fewest decimal places.