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Question:

In an experiment, four quantities a, b, c, and d are measured with percentage error 1%.

10

7

4

14

Solution:

Let P = a³b²cd.
The percentage error in P is given by:
ΔP/P * 100% = (3Δa/a + 2Δb/b + Δc/c + Δd/d) * 100%
Given that the percentage error in each quantity a, b, c, and d is 1%, we have:
Δa/a * 100% = 1%
Δb/b * 100% = 1%
Δc/c * 100% = 1%
Δd/d * 100% = 1%
Therefore,
ΔP/P * 100% = (3(1%) + 2(1%) + 1% + 1%) = 7%
The percentage error in P is 7%.