Significant Figures in Mathematical Operations The result of the mathematical operation cannot be expressed to any greater degree of certainty than the measured values used in the operation.

In a series of calculations ~ Carry the extra digits through the final results, then round g ÷ (35.60 mL – 22.40mL) = First:Then: mL55.6 ÷ = g/mL mL = 4.21 g/mL mL answer should have 3 sig figs as 55.6 had 3 sig figs

Adding and subtracting sig figs – the result should have the same number of decimal places as the least precise measurement used in the calculation!

Line up decimals and add g H2O (using significant figures) g salt g solution g solution is the least precise so the answer will have no more than one place to the right of the decimal.

Example Answer will have the same number of decimal places as the least precise measurement used cm 18.0 cm cm cm 9.62 cm cm Correct answer would be 71.9 cm – the last sig fig is “8”, so you will round using only the first number to the right of the last significant digit which is “7”.

Multiplication and division of sig figs – - your answer must be limited to the measurement with the least number of sig figs.

5.15 X sig figs 2 sig figs only allowed 2 sig figs so is rounded to 12 5 sig fig 2 sig figs Significant Figures

Multiplication and Division Answer will be rounded to the same number of significant figures as the measurement with the fewest number of significant figures cm x 1.4 cm = 6.38 cm 2 = 6.4 cm 2

28.0 inches 1 inch X 2.54 cm Computed measurement is cm Answer is 71.1 cm because the measurement of 28.0” had 3 sig figs - you DID NOT measure 1 inch or 2.54 cm – conversion already determined = =71.12 cm

More than one operation (1.245g g g)/7.5 Add = Then divide by 7.5 =