An experiment measures quantities a, b and c, | vedclass

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(A) The formula for the relative error in $X$ is given by: $\frac{\Delta X}{X} = \frac{\Delta a}{a} + 2\frac{\Delta b}{b} + 3\frac{\Delta c}{c}$ Given

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$\pm 13\%$

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(A) The formula for the relative error in $X$ is given by: $\frac{\Delta X}{X} = \frac{\Delta a}{a} + 2\frac{\Delta b}{b} + 3\frac{\Delta c}{c}$ Given percentage errors are: $\frac{\Delta a}{a} 	imes 100 = \pm 1\%$ $\frac{\Delta b}{b} 	imes 100 = \pm 3\%$ $\frac{\Delta c}{c} 	imes 100 = \pm 2\%$ Substituting these values into the error formula: $\frac{\Delta X}{X} 	imes 100 = \pm 1\% + 2(\pm 3\%) + 3(\pm 2\%)$ $\frac{\Delta X}{X} 	imes 100 = \pm 1\% \pm 6\% \pm 6\%$ To find the maximum percentage error,we add the magnitudes: $	ext{Maximum percentage error} = 1\% + 6\% + 6\% = 13\%$ Thus,the percentage error in $X$ is $\pm 13\%$.

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

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