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 5. 55.6g ÷ (35.60 mL – 22.40mL) = First: Then: 35.60 mL 55.6 ÷ 13.20 = 4.21212 g/mL 22.40 mL = 4.21 g/mL 13.20 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

150.0 g H2O (using significant figures) 0.507 g salt 150.5 g solution 150.5 g solution

150.0 is the least precise so the answer will have no more than one place to the right of the decimal.

ExampleAnswer will have the same number of decimal places as the least precise measurement used.

12.11 cm18.0 cm 1.013 cm31.132 cm 9.62 cm71.875 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.

5.15X 2.3 11.845

3 sig figs2 sig figsonly allowed 2 sig figs

so 11.845is rounded to 12

5 sig fig2 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.

4.56 cm x 1.4 cm = 6.38 cm2

= 6.4 cm2

28.0 inches 1 inchX 2.54 cm

Computed measurement is 71.12 cmAnswer 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 + 6.34 g+ 8.179g)/7.5

• Add

1.245 + 6.34 + 8.179 =

Then divide by 7.5 =