Have you ever thought that

money is actually countable instead of incountable, as we all have learned when we were young?

Every dollar is countable, up to every quarter/dime/cent/pence. And they told us money was not countable? I don't get it now. If money isn't countable, then how do we even use it? I can't pay you 5 dollars as I won't know how much is $5 exactly.

I mean, right?