Money can be counted and comes in standard unit sizes, so when money is used as a store of value and traded for something else, you can count the amount of money necessary to make the exchange.

You are not measuring anything, just finding an equivalence. There is nothing "rulerlike" about money.

The idea of measurement as my comment's parent used it, is at best a very sloppy way of thinking of what is going on. This may make sense in a colloquial sense, but it does not reveal anything about the mechanism that gives money value.

To give you an example, notes from a failed currency are worth only whatever the paper is worth, and do not (like silver coins) have alternate purpose as dental fillings which gives them intrinsic value.