Americans do love to divide into powers of two (½, ¼, and ⅛) rather then tenths. If anything they would be more likely to issue an eighth dollar as they phase out the penny, the nickle and the dime. And you would see prizes such as 4 dollar and ⅜ cents (and they would probably write it as $4–¢⅜).
EDIT: And petrol stations would display the prices in sixteenths, but charge a sixteenth more.