How the number is obtained
A pip is the smallest conventional price move: 0.0001 on most pairs, 0.01 on yen-quoted ones. That size is read from the instrument sheet, not guessed from the number of decimals displayed.
The value of a pip in the quote currency depends on no rate at all: one pip of EUR/USD is worth 0.0001 dollar per euro held, full stop. A standard lot of 100,000 euros is therefore 10 dollars a pip.
The rate only enters afterwards, to bring that amount back to your account currency. That is why the pip value of a dollar-quoted pair moves on a euro account, while it is fixed on a dollar account.