A physical quantity C is related to four other quantities p, q, r and s as follows: $$C = \dfrac{pq^2}{r^3 \sqrt{s}}$$. The percentage errors in the measurement of p, q, r and s are 1%, 2%, 3% and 2% respectively. The percentage error in the measurement of C will be ________ %.

A physical quantity $$C$$ is given by $$C = \dfrac{pq^{2}}{r^{3}\sqrt{s}}$$.

Write every factor with its power explicitly:
$$C = p^{1}\,q^{2}\,r^{-3}\,s^{-1/2}$$.

For a quantity expressed as a product of powers,
$$C = \prod_{i} A_i^{n_i}$$,
the fractional (or percentage) error rule is
$$\frac{\Delta C}{C} = \sum_{i} |n_i|\,\frac{\Delta A_i}{A_i}$$, because errors always add algebraically in magnitude.

Apply the rule to each variable:

• For $$p$$: power $$= 1$$ ⇒ contribution $$= 1 \times (\text{error in }p)$$
• For $$q$$: power $$= 2$$ ⇒ contribution $$= 2 \times (\text{error in }q)$$
• For $$r$$: power $$= 3$$ ⇒ contribution $$= 3 \times (\text{error in }r)$$
• For $$s$$: power $$= \tfrac{1}{2}$$ ⇒ contribution $$= \tfrac{1}{2} \times (\text{error in }s)$$.

Insert the given percentage errors:
$$\frac{\Delta C}{C}\% = 1 \times 1\% \;+\; 2 \times 2\% \;+\; 3 \times 3\% \;+\; \frac{1}{2} \times 2\%$$.

Compute each term:
$$1 \times 1\% = 1\%$$
$$2 \times 2\% = 4\%$$
$$3 \times 3\% = 9\%$$
$$\frac{1}{2} \times 2\% = 1\%$$.

Add them:
$$1\% + 4\% + 9\% + 1\% = 15\%$$.

Therefore, the percentage error in measuring $$C$$ is $$15\%$$.