Question

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

• A. $\pm 12.5\%$
• B. $\pm 7\%$
• C. $\pm 1\%$
• D. $\pm 4\%$

Answer 1

Answer: (A)

$\pm 12.5\%$

$X=\frac{a^{1/2}{b}^2}{c^3}$

We know from rules of error propagation in division and multiplication.

$\frac{\Delta X}{X}=\frac{1}{2}\frac{\Delta a}{a}+\frac{2\Delta b}{b}+\frac{3\Delta c}{c}$

$=\frac{1}{2}+2\times 3+3\times 2=12.5$%