Question:
Two lengths, a and b, are measured to be 51 ± 1 cm and 49 ± 1 cm respectively. In which of the following quantities is the percentage uncertainty the largest?
A. a + b
B. a – b
C. a x b
D. a : b
Answer: B
% uncertainty of a = (1 : 51) x 100% = 2.0 %
% uncertainty of b = (1 : 49) x 100% = 2.0 %
A. a + b = (51 + 49) ± (1 + 1) = 100 ± 2 cm
% uncertainty of (a + b) = (2 : 100) x 100 % = 2 %
B. a - b = (51 - 49) ± (1 + 1) = 2 ± 2 cm
% uncertainty of (a - b) = (2 : 2) x 100% = 100 %
C. & D.
When we multiply or divide quantities we add their fractional or percentage uncertainties, so:
% uncertainty of (a x b) and (a : b) = 2.0 % + 2.0 % = 4.0 %
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