Dimensionless units

[Ed Shaya]

I should add that in Pedro's system (if I may call it that), after doing 
a dimensional analysis that determines that a factor of c can be used to 
convert from one set of units to another, then the system must launch 
into a unit analysis to convert everything to SI base units so that c in 
units of m/s can be used.  One can devise equivalent variants of this 
but the point is that both unit analysis and dimensional analysis are 
done and they are different beasts.

Ed