A physical quantity X is related
Question:

A physical quantity X is related to four measurable quantities a, b, c and d as follows: X = a2 b3 c5/2 d–2. The percentage error in the measurement of a, b, c and d are 1%, 2%, 3% and 4%, respectively. What is the percentage error in quantity X? If the value of X calculated on the basis of the above relation is 2.763, to what value should you round off the result.

Solution:

The given physical quantity, X = a2 b3 c5/2 d–2

Percentage error in X = (∆x/x)(100)

Percentage error in a = (∆a/a)(100) = 1%

Percentage error in b = (∆b/b)(100) = 2%

Percentage error in c = (∆c/c)(100) = 3%

Percentage error in d = (∆d/d)(100) = 4%

Maximum percentage error in X = ±23.5%

X should have two significant values, therefore, X = 2.8

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