I am writing a lab for my high school physics class, and I calculated the change in gravitational potential energy in one trial to be $\Delta E_\text{P}=0.27\text{ J}$. The height from which the mass dropped was only measured to 2 significant figures, with an uncertainty of 1 cm. Now, in order to calculate the uncertainty in the measurement, I did the following. $$\frac{\Delta \left(\Delta E_\text{P}\right)}{\Delta E_\text{P}}=\left[\frac{\Delta\left(\Delta h\right)}{\Delta h}\right]\Longleftrightarrow\Delta \left(\Delta E_\text{P}\right)=\Delta E_\text{P}\left[\frac{\Delta\left(\Delta h\right)}{\Delta h}\right]=mg\Delta h\left[\frac{\Delta\left(\Delta h\right)}{\Delta h}\right]=mg\Delta\left(\Delta h\right)=\left(0.050\text{ kg}\right)\left(9.81\text{ m s}^{-2}\right)\left(0.01\text{ m}\right)=0.004905\text{ J}$$
In significant figures, this would be expressed as 0.005 J; however, my calculation for the change in gravitational potential energy only has 2 decimal places of precision, meaning I would further have to round the uncertainty to 0.01 J. I would be ok with this, except that 0.004905 is closer to 0 than it is to 1. Which value should I express my uncertainty as?
If I express it as 0, should I give precision to the 0? For example, 0 or 0.00 J.
Also, I know there are way better ways to express precision and significant figures, but this is what we are taught to do in class so I would like to stick to that.