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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.
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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
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Adding and subtracting sig figs
– the result should have the same number of decimal places as the least
precise measurement used in the calculation!
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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.
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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”.
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Multiplication and division of sig figs –
- your answer must be limited to the measurement with the least
number of sig figs.
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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
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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
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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
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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 =