Rules for significant figures

In general, a calculated value cannot be more precise than the values used to compute it. The rules regarding significant figures in calculations are as follows:

    • Significant figures of conversion factors and physical constants are not evaluated in determining the precision of the computed result, e.g. 2 moles of an ideal gas occupy 2 x 22.4 = 44.8 dm3 at standard temperature and pressure (2 is the conversion factor).
    • As mentioned, a calculated value cannot be more precise than the values used to compute it. Therefore, when multiplying and dividing numbers, the result usually has the same significant figures as the factor with the least number of significant figures.

For example, 2.1 x 4.01 = 8.421, the result should be rounded off to 2 significant figures, i.e. 8.4. However, if we round off the answer of (25.0 cm3 x 0.100 mol dm3)/28.5 cm3 = 0.0877193 mol dm3 to 3 significant figures, the answer 0.0877 mol dm3, which is a  calculated concentration, will have a precision of 1 in 877, which is more precise than the measured concentration of 0.100 mol dm3, which has a precision of 1 in 100. Therefore, the answer should instead be rounded off to 2 significant figures, i.e. 0.088 mol dm3.

    • When adding and subtracting numbers, the values that are used to compute the result must have the same unit of measurement, e.g. 1.02 g + 2.8216 g + 766.9 g = 770.7416 g. The values 1.02 g, 2.8216 g and 766.2 g, having different decimal places, must be measured using instruments of different precisions, with the instrument giving the last value being the least precise (i.e. a weighing instrument that can only measure values of up to one decimal place). Hence, the result cannot be more precise than 766.2 g and should be reported with one decimal place: 770.7 g.¬†Therefore, when adding and subtracting numbers, the result has the same number of decimal places as the factor with the least number of decimal places.
    • For multi-step calculations, it is a good habit to maintain extra significant figures for answers in the intermediate steps, and only round off the final answer to the appropriate number of significant figures.

 

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