Question

A physical quantity $\times$ is calculated from the relation $x=\frac{a^2{b}^3}{c\sqrt{d}}$. If percentage error in $a,b,c$ and $d$ are $2\%,1\%,3\%and4\%$ respectively. What is the percentage error in $x$?

Answer 1

Percentage error in x, $\frac{\Delta x}{x}\times 100=$ $2\times \frac{\Delta a}{a}\times 100$ $+3\times \frac{\Delta b}{b}\times 100$ $+\frac{\Delta c}{c}\times 100$ $+\frac{1}{2}\times \frac{\Delta d}{d}\times 100$

Or $\frac{\Delta x}{x}\times 100=$ $2\times 2$ $+3\times 1$ $+3$ $+\frac{1}{2}\times 4=12\%$