Moral of the story is that numbers with dimensions totally arbitrary. In theoretical physics you often want to find a small parameter to do a Taylor expansion a

Moral of the story is that numbers with dimensions totally arbitrary. In theoretical physics you often want to find a small parameter to do a Taylor expansion and make some mathematical expression simpler. A small parameter is a number much less than one, but if we have a quantity with the units of metres for example, we cannot say "r is much less than 1" because you can't compare a number with dimensions to one. You could always pick your units such that the number is much less than 1. What you instead do is find some _ratio_ of quantities that is much less than one, because then the units cancel and you have a dimensionless quantity that you can then compare to 1.