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CHAPTERS BY WACEK KIJEWSKI

# CHAPTER VIII:  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.

Wacek Kijewski
Metric Fun
"SI Units, Conversion and Measurement Skills"
PO Box 2358 George 6530 South Africa
tel/fax: +27 44 884 0486

About the Author

Wacek Kijewski: born in Poland, studied electronics, telecommunication, acoustics and pedagogy. He taught science in Poland, Hungary and became Lecturer and Principal Tutor in Nigeria and Botswana.
Mr. D.D. Kuhlmann, Ag Registrar, University of Botswana (UB): “Dr W. Kijewski has performed his duties very satisfactorily and proved that he is an excellent teacher with substantial relevant experience. He has an admirable character which coupled with his professional integrity enabled him to established an excellent rapport with students.”

Dr. L.S. Molema, English Dept., UB: “Students speak warmly of him, especially his capacity for making them understand and feel confident in a subject that they had previously been inadequately prepared for and were therefore scared of. I have just finished editing the proofs of his new book: “S I Units, Conversion and Measurement Skills” in which his teaching style, so popular with his students, is evident.”

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