Question: In an experiment, four quantities $a,b,c$ and $d$ are measured with percentage errors $1\%$, $2\%$, $3\%$ and $4\%$ respectively. Quantity $P$ is calculated as

$$
P=\frac{a^{3}b^{2}}{cd}.
$$

The percentage error in $P$ is:
a. $7\%$
b. $4\%$
c. $14\%$
d. $10\%$

Answer. c. $14\%$

Solution.

$
P = \frac{a^{3} b^{2}}{cd}
$

% error in $P$ is

$
\frac{\Delta P}{P} \times 100 = \left[ 3\left(\frac{\Delta a}{a}\right) + 2\left(\frac{\Delta b}{b}\right) + \frac{\Delta c}{c} + \frac{\Delta d}{d} \right] \times 100
$

$= [3 \times 1\% + 2 \times 2\% + 3\% + 4\%] = 14\%$