Did you ever look at the Constitution of the United States? It uses the word "dollar" just as it uses the word "year." Neither are defined because everyone in the late 18th Century English speaking world understood what these words meant. A "dollar" was a Spanish silver coin. One of the first act of the Congress was the Coinage Act of 1792 where an American Dollar was defined. In doing this Congress collected a whole bunch of Spanish dollars, and determined that on average each contained 371.25 grains of fine silver. Congress then defined an American dollar as this same 371.25 grains of silver. I don't believe this has ever changed.
Maybe you've heard about gold, but gold was always denominated in "Eagles" with one eagle being set equivalent to ten dollars. From time to time people (like William Jennings Bryant) argued about how much gold should be in an eagle, but the dollar remained as it was.
It is amusing to research the history of the Art I, Sect 10 Clause 2 of the US Constitution: "No State shall make any Think other than Gold and Silver a Tender in payment of Debts." Madison, in the Federalist Papers says the clause was included to "protect the people from the pestilent effects of paper money."
FTR, Federal Reserve Notes are denominated in dollars. They are not dollars.
ML/NJ
Of course, the result of having your money strictly on the basis of precious metals means that the money supply can only expand as more metals are discovered, mined, refined and minted. The effect is deflationary as products chase a limited amount of money, people who have money don't spend it (because they'll get more from a desperate seller tomorrow) and counterfeiting becomes more attractive.