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Is there a generally accepted term for fractions of Currency Units?
The Coinage Act of 1792 of the Continental Congress established that the lowest money of account for the United States is one-thousandth (1/1000) of a dollar. This sub-unit is the mille (also written mil, mill). Other sub-units  given by the act are the disme for one-tenth (1/10) of a dollar (for which, etymologically, is the origin of the word dime), and the cent for one-hundredth (1/100) of a dollar. The ten-thousandth of the dollar value is taken on account by a few financial organizations, but has no official given term. For the monetary value of USD 27.4955, it may be quoted as twenty-seven dollars, forty-nine cents, and five-and-a-half milles.