Question

An experiment measures quantities $a$, $b$ and $c$, and quantity $X$ is calculated from $X= ab^2/c^3$. If the percentage error in $a$, $b$ and $c$ are $\pm 1\%$, $\pm 3\%$ and $\pm 2\%$, respectively, then the percentage error in $X$ will be

• A. $\pm 13\%$
• B. $\pm 7\%$
• C. $\pm 4\%$
• D. $\pm 1\%$

Answer 1

Answer: (A)

$\pm 13\%$

Answer 2

$\frac{\Delta x}{x}=\frac{\Delta a}{a}+2\frac{\Delta b}{b}+3\frac{\Delta c}{c}$
$=\pm1\%+2\left(\pm3\%\right)+3\left(\pm2\%\right)$
$=\pm1\%\pm6\%\pm6\%$
$=\pm13\%$