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# Chapter 09 Compound Errors

1. Compound errors in additions and subtractions

Rule 1:  When finding the sum of, or the difference between the values of two (or more) measurements, the absolute error of the result is found by taking the sum of the absolute errors of the measurement.

E.g. 1:

Let a = 50.5 ± 0.5 mm and b = 10.20 ± 0.05 mm

a + b = (50.5 mm + 10.20 mm) ± (0.5 mm + 0.05 mm) = 60.7 ± 0.55 mm

Rounding off the error to one significant figure and the value to the same level of significance, we get:

a + b = 60.7 ± 0.6 mm

E.g. 2:

a – b = (50.5 mm - 10.20 mm)± (0.5 mm + 0.05 mm) = 40.30 ± 0.55 mm

a - b = 40.3 ± 0.6 mm

2. The number of significant figures in errors

Rule 2: The error of a quantity in a measurement as well as in the final answer is expressed by one significant figure.

While computing the errors in the last examples, we rounded off each error to one significant digit. This is due to the fact that uncertainty is always in the final (significant) figure of the reported value.

Do you like anecdotes, interesting and challenging problems, fun facts, puzzles, jokes related to metric system and measurement? Read them in the 2006 on-line edition of "SI Units, Conversion and Measurement Skills",186 pp.