First slide

Errors

Question

In an experiment, four quantities a, b, c and d are measured with percentage error 1%, 2%, 3% and 4% respectively. Quantity P is calculated as follows $P = \frac{a^{3} b^{2}}{c d}$ . % error in P is

Moderate

A

7%
B

4%
C

14%
D

10%

Solution

$\begin{aligned} As P = \frac{a^{3} b^{2}}{c d} \\ % error in P is \\ \begin{aligned} \frac{Δ P}{P} & \times 100 = [3 (\frac{Δ a}{a}) + 2 (\frac{Δ b}{b}) + \frac{Δ c}{c} + \frac{Δ d}{d}] \times 100 \\ = [3 \times 1 % + 2 \times 2 % + 3 % + 4 %] = 14 % \end{aligned} \end{aligned}$

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