Why it is important to convert units prior to calculation?

It's not. What it is, often, is easier.

You should know by now that you need to be working with a consistent set of units. This means that your unit for velocity is your unit for length divided by your unit for time…and your unit for acceleration is your unit for velocity divided by your unit for time…and your unit for force is your unit for acceleration multiplied by your unit for mass…and your unit for energy is your unit for force multiplied by your unit for length…and your unit for power is your unit for energy divided by your unit for time…and so on.

In this way, your calculations will automatically yield answers in the correct units.

SI makes things very easy because of everything being consistent and base 10 with the metric prefixes. It also was standardized nicely from the start. It also is based upon a number of important physical constants…so, for example, water at room temperature is about 1g/cc and it has a a specific heat of 1 calorie per gram and 100 degrees between freezing and boiling.

These days, all other systems of measurement are based on SI units, anyway, so you'll be hard pressed to find a better and easier system to work with.

i believe the answer is a

a) electrical > light, sound, and thermal< < < <

) the mechanical energy of the firefighter moving.< < < < a) electrical > light, sound, and thermal< < < <

c) both a and b.