Question

A physical quantity $x$ is calculated from the relation $x=\frac{a^2{b}^3}{c\sqrt{d}}$. If the percentage error in a, b, c and d are $2\%,1\%,3\%$ and $4\%$, respectively, what is the percentage error in $x$?

Answer 1

As x = $\frac{a^2{b}^3}{c\sqrt{d}},$
$\therefore \frac{△x}{x}=\pm [2\frac{△a}{a}+3\frac{△b}{b}+\frac{△c}{c}+\frac{1}{2}\frac{△d}{d}]\frac{△x}{x}\times 100$
$\pm [2\times 2\%+3\times 1\%+\frac{1}{2}\times 4\%]$
=$\pm [4\%+3\%+3\%+2\%]=\pm 12\%$.