Question

The percentage errors in a, b, c and d are $4\%,3\%,2\%$ and $1\%$ respectively. Calculate the percentage error in x, if $x=a{b}^3{c}^{-1/2}{d}^{-3/2}$.

Answer 1

$X=\frac{A^2{B}^3}{c\sqrt{D}}=\frac{A^2{B}^3}{{CD}^{1/2}}$

$\frac{△X}{X}\times 100‰=2\frac{△A}{A}+3\frac{△B}{B}+\frac{△C}{C}+\frac{1}{2}+\frac{△D}{D}$

$\frac{△X}{X}\times 100‰=2\times 4$

$\frac{△X}{X}\times 100‰=8$

$\frac{△X}{X}\times 100‰=\pm 19.5$