A student measures a pendulum's length as l = (0.800 ± 0.002) m, and times 30 swings as (53.7 ±…

Step 1. Period. $T = \dfrac{53.7\ \text{s}}{30} = 1.79\ \text{s}$.

Step 2. g. $g = \dfrac{4\pi^2 \times 0.800\ \text{m}}{(1.79\ \text{s})^2} = 9.86\ \text{m/s}^2$.

Step 3. Errors. Length: $\dfrac{0.002\ \text{m}}{0.800\ \text{m}} = 0.25\%$. Time: $\dfrac{0.2\ \text{s}}{53.7\ \text{s}} = 0.37\%$, doubled to $0.74\%$. Total $\approx 1.0\%$.