What are the names, conventions, methods, and resources for converting physical units from one form to another, especially into and out of the SI?

For example, car gasoline “mileage” in the US is customarily written as miles per gallon. You could convert this into kilometers per liter. But liters are themselves convertable into cubic meters, so you could also convert car gasoline use into kilometers per cubic meters, or into inverse square meters. Since meters are a fundamental unit of the SI, there isn’t any further conversion you could do that would further reduce this to a basic SI measurement. There is even a conceptual interpretation of this: if some model car has gasoline consumption efficiency of “X per square meter”, then you could have X of these cars all plumbed together to drive along some highway with a one-square-meter trough of gasoline running alongside it, and they would just consume this trough’s contents as they rode along next to it together.

Also, though there are many possible unit combinations to represent a given physical measurement, only one of them would be this furthest reduced one. That means there is exactly one ultimate unit combination for each possible measurement. It is interesting to study the SI and consider alternative systems, because this doesn’t represent some underlying physical truth about measurement, but rather is just a logical consequence of having a consistently defined unit system with designated base units, and there are a few interesting alternative systems laid out with other designated base units.

Is anything I said incorrect or misleading or confusing? What do you call this furthest possible reduction to base SI units? Are there web sites or utility programs that do such a reduction?

Thanks!