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Question
A physical quantity X is related to four measurable quantities a, b, c and d as follows: X = a2 b3 c5/2d–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
Given, physical quantity is X = a2 b3 c5/2d–2
The maximum percentage error in X is
`(Δx)/x xx 100 = +- [2((Δa)/a xx 100) + 3((Δb)/b xx 100) + 5/2((Δc)/c xx 100) + 2((Δd)/d xx 100)]`
= `+- [2(1) + 3(2) + 5/2 (3) + 2(4)]%`
= `+- [2 + 6 + 15/2 + 8]`
= `+- 23.5%`
∴ Percentage error in quantity X = ± 235%
Mean absolute error in X = ± 0.235 = ± 0.24 ......(Rounding-off upto two significant digits)
The calculated value of x should be round-off up to two significant digits.
∴ X = 2.8
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