Chemistry · Ch 2 — Introduction to Analytical Chemistry

Significant figures

2.3.3

Significant figures

Every measured value carries some uncertainty, and that uncertainty in turn carries through into any result calculated from it. The way this uncertainty is communicated is by controlling the number of significant figures quoted in a value: the significant figures in a measurement or a calculated result are the digits that are known with complete certainty, plus exactly one further digit that is understood to be uncertain (estimated). For a burette reading recorded as $10.2 \pm 0.1$ mL, for instance, the digits '1' and '0' are certain, while the final digit '2' is the one uncertain digit, with an uncertainty of $\pm 0.1$ mL matching the burette's least count. In a real experimental calculation, several different quantities are usually measured with several different pieces of equipment, each of which has its own least count and therefore its own number of significant figures; a fixed set of rules (covered in the next section) is used to decide …

Misc Problem 2.6Calculating absolute deviation and relative deviation

Worked out. Worked example: three identical samples of potassium chlorate are decomposed, giving 3.87 g, 3.95 g and 3.89 g of oxygen. Mean = $(3.87 + 3.95 + 3.89)/3 = 3.90$ g (rounded). The absolute deviation of each reading from the mean is: sample 1, $|3.87 - 3.90| = 0.03$ g; sample 2, $|3.95 - 3.90| = 0.05$ g; sample 3, $|3.89 - 3.90| = 0.01$ g. The mean absolute deviation is the average of these: $(0.03 + 0.05 + 0.01)/3 = 0.03$ g, so the result is written as $\pm 0.03$ g. Relative deviation = (mean absolute deviation / mean) × 100% = $(0.03/3.90) \times 100\% \approx 0.8\%$ , which tells us the measurements were reproduci …

Misc Problem 2.7Counting the significant figures in given measurements

Worked out. Worked example applying the significant-figure counting rules to seven quantities: (a) 4.065 m has 4 significant figures (all non-zero digits, plus the zero sandwiched between two non-zero digits, are significant); (b) 0.32 g has 2 significant figures (the leading zero before the decimal point only fixes the decimal position and is not significant); (c) 57.98 cm3 has 4 significant figures; (d) 0.02 s has 1 significant figure (leading zeros are never significant); (e) $4.0 \times 10^{-4}$ km has 2 significant figures (both digits of the coefficient in scientific notation count); (f) 604.0820 kg has 7 significant figures (the internal zero and the trailing zeros after the decimal point are all significant); (g) $307.100 \times 10^{-5}$ cm has 6 significant figures (all digits of the coefficient …

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