I had a dealer at a local stamp show (try to) explain fractional currency to me. I've always liked them because of their designs, and he noticed I was eyeing an example he had for sale. After telling him it was way beyond my budget, he started to explain their use. I only wish my short term memory was better, because he knew a LOT.
It seemed to have a lot to do with currency issues during the Civil War. Should be easy to locate info online.