It's more accurate to say "never use floats for accounting." You should be able to state with 100% certainty how much money you owe no matter how much money you owe.
Not 100%. There's gotta be a precision cutoff somewhere between $1 and the inverse of Avogadro's number.
I'll cede this point. If you're accounting for the quantity of pennies down to the precision of individual penny atoms then your accounting must be accurate to within the quantity of penny atoms that are rubbed off the penny during normal handling during the transaction.