> 2 mW / 1 mW = 2 = 10^(3/10) = 3 dBm

It's worth noting that this is wrong, in exactly the way that makes decibels confusing. 3 dBm is an absolute power figure (about 2 mW). 2 mW / 1 mW is a ratio of 2 (about 3 dB).

2 mW / 1 mW = 2 = 10^(3/10) = 3 dB.

2 mW = 2 * 1 mW = 10^(3/10) * 1 mW = 3 dB (1 mW) = 3 dBm.

Similarly, but in a very different context:

I have to teach non-engineers C programming for an undergrad course, which is basically trying to teach very explicit attention to punctuation (among many other things). "Watch those double quotes!", "single quotes, not double!", "where's your semi-colon??", and so on.

Then, three weeks into the course, we're passing values by reference with &, and I get the question, "isn't that scanf missing the and-sign in front of the string name?", and I'm forced to answer, "that punctuation doesn't matter, this time," because the C standard makes & do nothing in front of a string specifically because so many people were confused about that fact that a string's variable name is already passing by reference.

Yeah, that's a better way of thinking about it. That way you don't have any phantom bookkeeping like the way I was taught. The units are still right there.