# The percentage errors in quantities P, Q, R and S are 0.5%, 1%, 3% and 1.5%respectively in the measurement of a physical quantity $A= \frac{P^{3}Q^{2}}{\sqrt{R}S}$

For maximum percentage error, differentiate and divide the equation by itself

$\frac{\Delta A}{A} =3 \frac{\Delta P}{P} +2\frac{\Delta Q}{Q} +\frac{1}{2}\frac{\Delta R}{R}+\frac{\Delta S}{S}$

$\frac{\Delta A}{A} = 6.5 \%$

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