Comment by eru

> Now, Kg is a measure of mass (or weight, depending on who you are asking), which throws density into the equation, [...]

It's the other way round: chemically how much energy you get from burning your fuel is almost completely a function of mass, not of volume. (And in fact, you aren't burning liquid fuel either, in many engines the fuel gets vaporised before you burn it, thus expanding greatly in volume but keeping the same mass.)

> [...] which throws density into the equation, which is proportional to the temperature [...]

For an ideal gas, sure. But not for liquid fuels.

> "litres-of-fuel per km-driven" (Volume/Distance) is still fully reductible to an area: litres is still a volume (1 cubic decimeter) and km is still a distance (1x10⁴ dm) Maybe you meant that the other way around? Distance/Volume (as in Miles/gallon) is an Area⁻¹ (Distance⁻²), which is more difficult to imagine in space.

I don't think that the reciprocal is a problem. No, what I mean is that you can't cancel fuel with driving. Litres-of-fuel is a different unit than distance-driven ^ 3. Similar to how torque and energy are different physical quantities that you can't cancel willy-nilly, despite their units looking similar.

You might find a physical interpretation for an adventurous cancelling, and that's fine. But that's because you are looking behind the raw unadorned units at the physics, and basing your decision on that.

Units are a very stripped down look at physics. So units working out are necessary for cancelling to make sense, but not sufficient.