And as Colibri noted, the cent was theoretically divided into 10 mill(e)s. (Some tax assessments are still made in mills, though there were never mill coins.) And it was once proposed that, consistent with this decimal system, the next step up from the eagle be the “union” (10 gold eagles = 1 large gold union). So we sort of almost had a six-unit, three-metal system.
The American di(s)me is a unit unto itself. A “nickel,” on the other hand, is just a five-cent piece, a denomination.
This gives me an opportunity to advance my solution to the “penny problem”: let the dime be our smallest unit. Just drop “cents,” or render them theoretical, like mills.
Some have advocated ending minting of the cent but maintaining “nickels” and rounding off all sums to the nearest five cents. This leads to to the perception that somebody is being stiffed a little on each transaction, and it just feels conceptually awkward to have a system in which an actual denomination is a multiple of a theoretical unit (imagine if your pocket change all these years had included five-mill coins). Abandoning physical cents entirely (including the five-cent piece), on the other hand, is a recalibration of the scale to a new unit. Pricing in dollars and dimes is no more “rounding” than present pricing in dollars and cents.