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How can I understand “thirty-seconds of a dollar”?

If the unit price were $0.25, it would be put into words as quarters of a dollar (or quarters, in normal speech). If it were $0.20, it would be fifths of a dollar. Following this pattern, thirty-seconds of a dollar means “a unit price of $.03125”. It sounds odd because only the US Treasury (as far as I know) uses this particular measurement.