In an experiment to determine the acceleration due to gravity ( g )...

The formula for acceleration due to gravity using a simple pendulum is:
$g = \dfrac{4\pi^2 L}{T^2}$

The maximum percentage error in $g$ is given by:
$\dfrac{\Delta g}{g} \times 100 = \dfrac{\Delta L}{L} \times 100 + 2 \left( \dfrac{\Delta T}{T} \times 100 \right)$

For the length measurement:
Measured length, $L = 20.0\text{ cm}$
Least count, $\Delta L = 1\text{ mm} = 0.1\text{ cm}$
Percentage error in length = $\dfrac{0.1}{20.0} \times 100 = 0.5\%$

For the time measurement:
Total time measured, $T_{total} = 100\text{ s}$
Least count, $\Delta T_{total} = 1\text{ s}$
Percentage error in time = $\dfrac{1}{100} \times 100 = 1\%$

Substituting these into the error equation for $g$:
$\dfrac{\Delta g}{g} \times 100 = 0.5\% + 2(1\%) = 0.5\% + 2\% = 2.5\%$

Answer: $2.5\%$