Arithmetic and Significant Figures

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Rules for Multiplication and Division

Chem 1115

1. In calculations involving measurements, only the measurements are considered when determining the correct number of signficant figures for the answer. Ignore exact values such as conversion factors.
2. The answer must contain the same number of significant figures as the measurement with the fewest significant figures.

Chem 1215

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Example:

11.510 g/7.85 mL = 1.46624204 g/mL = 1.47 g/mL

The answer is rounded to three significant figures because 7.85 contains 3 significant figures while 11.510 contains five signficant figures.

Rules for Addition and Subtraction

1. In calculations involving measurements, only the measurements are considered when determining the correct number of signficant figures for the answer.
2. The answer must contain the same number of decimal places as there are in the measurement with the fewest decimal places.

Example:

125.1 g + 1.300 g + 0.27 g = 126.670 g = 126.7 g

The answer is rounded to 1 decimal place because the three masses that are being added have 1, 3, and 2 decimal places, respectively. Report the answer to the fewest number of decimal places.

Practice Problems

Perform the following calculations using the rules that apply to calculations involving measurements (i.e. apply the rules for significant figures.

1. 2.501 + 12.40 - 3.996 =
2. 25.3 x 1.0 x 2.75 =
3. (2.503 - 2.303)/2.303 =
4. 15.00/1.50 =