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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

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significant figures in mathematical operations

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
In a series of calculations ~

Carry the extra digits through the final results, then round

  • 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 mLanswer should have 3

sig figs as 55.6 had 3 sig figs

slide3

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
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.

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

12.11 cm

18.0 cm

1.013 cm

31.132 cm

9.62 cm

71.875 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
Multiplication and division of sig figs –

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

slide7

5.15

X 2.3

11.845

Significant Figures

3 sig figs

2 sig figs

only allowed 2 sig figs

so 11.845

is rounded to 12

5 sig fig

2 sig figs

multiplication and division
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

slide9
28.0 inches 1 inch

X 2.54 cm

Computed measurement is 71.12 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
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 =