At least in some parts of the US, the traditional explanation of "two bits" for the quarter (US version) is that there was very little coinage available, so a "dollar" coin was frequently cut into pieces to make change.

Cut across a diameter, it's easy to make eight "bits" by cutting each piece in half, each half in half again, and the each of the four pieces in half; but anything smaller is hard to keep track of and it's hard to tell if one was made by "honest cuts." (And only excellent geometers of the time could possibly cut one in tenths, although twelths would have been possible.)

For much of our history (a fair fraction of how long we've been around) there was no "official" coinage available for widespread use, and each bank, or sometimes each individual shopkeeper**, issed their own. (One might assume that wooden dollars were a lot easier to cut into "bits" than metal ones, but "local coins" made out of local materials could be made in many more denominations?)

This explanation is frequently seen in historical reports, but verification would be difficult due to the number of conflicting fantasies.

"Explaining" US slang terms on the basis of British precedents is not generally as reliable as some may assume, although "every good lie needs at least a half truth buried within it."

** "or saloon" might be added. A belt buckle I've worn for about 50 years is claimed to be a derivative from a "coin" used for change at "Rosie's Saloon and Good Time Emporium - Good for one free redeye and ride." (If you could only get change in "house coin" you had to come back and spend the change at the same place?)

John