Significant Figures: Rules and Calculation

• Significant figures are all digits of a measured quantity, including the certain one, except for the last digit, which is estimated.

Counting Significant Figures

• All non-zero digits are always significant.
• Interior zeros (zeros between nonzero numbers) are significant.
• Leading zeros (zeros at the beginning of a number) are not significant.
• Trailing zeros (zeros at the end of the number) are significant if a decimal point is present in the number or if they carry overbars.
• Trailing zeros are not significant otherwise.
• Exact numbers have an unlimited number of significant figures.

Significant Figures in Calculation

Multiplication and Division

• When multiplying or dividing measurements with significant figures, the result has the same number of significant figures as the measurement with the lowest number of significant figures.
• Example: 5.02 (3 sig. figs.) * 89.665 (5 sig. figs.) * 0.10 (2 sig. figs.) = 45.0118 which rounds off to 45 (2 sig. figs.).
• Example: 5.892 (4 sig. figs.) / 6.10 (3 sig. figs.) = 0.96590 which rounds off to 0.966 (3 sig. figs.).

Addition and Subtraction

• When adding or subtracting measurements with significant figures, the result has the same number of decimal places as the measurement with the lowest number of decimal places.
• Example: 2.0345 (4 d.p.) + 0.07 (2 d.p.) + 2.9975 (4 d.p.) = 5.4125 which rounds off to 5.41 (2 d.p.).
• Example: 5.9 (1 d.p.) - 2.221 (3 d.p.) = 5.679 which rounds off to 5.7 (1 d.p.).