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If $Q = \frac{{{X^n}}}{{{Y^m}}}$ and $\Delta X$ is absolute error in the measurement of $X, \Delta Y$ is absolute error in the measurement of $Y,$ then absolute error $\Delta Q$ in $Q$ is
$\Delta Q = \pm \,\,\left( {n\frac{{\Delta X}}{X} + m\frac{{\Delta Y}}{Y}} \right)$
$\Delta Q = \pm \,\,\left( {n\frac{{\Delta X}}{X} + m\frac{{\Delta Y}}{Y}} \right)Q$
$\Delta Q = \pm \,\,\left( {n\frac{{\Delta X}}{X} - m\frac{{\Delta Y}}{Y}} \right)Q$
$\Delta Q = \pm \,\,\left( {n\frac{{\Delta X}}{Y} - m\frac{{\Delta Y}}{X}} \right)Q$
Solution
Here, maximum fractional error is $:$
$\frac{\Delta Q}{Q}=\pm\left(n \frac{\Delta X}{X}+m \frac{\Delta Y}{Y}\right)$
$\therefore$ Absolute error in $\mathrm{Q},$ i.e.
$\Delta \mathrm{Q}=\pm\left(\mathrm{n} \frac{\Delta \mathrm{X}}{\mathrm{X}}+\mathrm{m} \frac{\Delta \mathrm{Y}}{\mathrm{Y}}\right) \mathrm{Q}$
