[ChainOfFools]

I think we may be talking at cross purposes. I specifically used the number one because it behaves like a unit here. unlike 2 or any other number, 1 is also the standard 1D unit vector, so 1apples is indeed the same quantity as apples/1, but because it is a unit we usually imply its presence rather than express it explicitly as above.

watts/unit thus seems fine to me, whatever the unit may be, even if it itself is derived from time. watts per day would just work out to joules/second/1/24*60*60, making 1 watts per day a derived unit that expresses joules/84600 seconds, or an instantaneous rate of one 84600th of a joule.