A physical quantity P is given as P = a ^ 2 b ^ 3 c d . The...

The given quantity is $P = \dfrac{{a}^{2}{b}^{3}}{c\sqrt{d}}$.

The percentage error for a quantity can be given by the formula $\dfrac{∆ x}{x} \times 100$.

Relation of the relative errors will be,

\left(\dfrac{\DeltaP}{P}\right) = \left[\left(\dfrac{2\Deltaa}{a}\right) + \left(\dfrac{3\Deltab}{b}\right) + \left(\dfrac{\Deltac}{c}\right) + \left(\dfrac{1}{2}\dfrac{\Deltad}{d}\right)\right]$</p><p>Hence, the percentage error is calculated by substituting the values,</p><p>$\left(\dfrac{\DeltaP}{P}\right) \times 100 = \left(2 \times 1\right) + \left(3 \times 2\right) + 3 + \left(\dfrac{1}{2} \times 4\right) = 13 %.