$A$ physical quantity $P$ is given as $P = \frac{a^2 b^3}{c \sqrt{d}}$. The percentage errors in the measurement of $a, b, c,$ and $d$ are $1 \%, 2 \%, 3 \%,$ and $4 \%$ respectively. The percentage error in the measurement of quantity $P$ will be $.......\%$.

"It is advisable to use an instrument with the smallest possible least count." Explain this statement.

The density $\rho$ of a uniform cylinder is determined by measuring its mass $m$, length $l$ and diameter $d$. The measured values of $m, l$ and $d$ are $97.42 \pm 0.02 \text{ g}$, $8.35 \pm 0.05 \text{ mm}$ and $20.20 \pm 0.02 \text{ mm}$, respectively. The calculated percentage fractional error in $\rho$ is . . . . . . . (in $\%$)

To estimate $g$ from $g=4 \pi^2 \frac{L}{T^2}$,the error in the measurement of $L$ is $\pm 2 \%$ and the error in the measurement of $T$ is $\pm 3 \%$. The error in the estimated $g$ will be

State the rule for the error in the result due to multiplication and division of two physical quantities.

Can error be completely eliminated?