Considering $g = \pi$ and its approximation $g_h = \frac{22}{7}$ I am trying to find the absolute error and relative error.
Here are my workings, this is the first tie doing this sort of problem so I am not sure if this is correct or not.
$$E_{abs} = \left|\pi - \frac{22}{7}\right| = 0.00126 \approx 0.0013$$
$$E_{rel} = \left| \frac{\pi - \frac{22}{7}}{\pi}\right| = 0.000402 \approx. 0.0004$$
Looking to see if these workings are correct, thanks!
You have used the definitions of absolute and relative error correctly.
One criticism: I suggest you modify your notation to show that the error is not exactly $0.000402$, perhaps by using ellipsis.
$$E_{rel} = \left| \frac{\pi - \frac{22}{7}}{\pi}\right| = 0.000402\color{red}{\dots} \approx 0.0004$$