Panama 1 1/4 centesimos. It's hard to imagine any reason to use such a silly denomination. I know it's half of the 2 1/2 centesimos, which is half of the 5 centesimos, but come on.
It would make sense if things cost so little that 5 centimos was considered a lot. The US did have 1.25 cent postage stamps at one time, after all.
You also have quirky situations as in Elizabethan England when a three farthings (3/4 of a penny) was introduced. The reason for this was the impractically small size of a silver farthing based on it's intrinsic value having to equal it's face value. So you handed over a penny and received 3/4d in change, or alternatively used a three farthings and received a halfpenny.
These fractional denominations are just weird to me. I understand it comes from splitting a larger denomination like 25 or 5 in half but it's still strange when you think of it in terms of real prices. Here's two more.
The farthing situation was resolved in 1613 with the introduction of the copper Harington farthings, but they weren't popular. If you mean we should have had the cent as the smallest unit, then why did the US have 1/2c? When the newly independent country was designing its own currency, the logical starting point would have been to call the smallest value item 1 whatever, and build from there. Building a decimal system with additional fractional values just doesn't make sense.
So if you were to make a purchase that cost 1 centesimos and paid with the 1-1/4 centesimos, how did the proprietor give you your 1/4 centesimos change?
I think the Spanish tradition of dividing money into eighths persisted after decimalization, with the decimo serving a similar role to the old real. So 2½ and 1¼ centavos would have been natural divisions. Even in the Western US, the division of dollars into eighths persisted for a long time. Here's Robert Louis Stevenson on it: "In the Pacific States they have made a bolder push for complexity, and settle their affairs by a coin that no longer exists – the bit, or old Mexican real. The supposed value of the bit is twelve and a half cents, eight to the dollar. When it comes to two bits, the quarter-dollar stands for the required amount. But how about an odd bit? The nearest coin to it is a dime, which is, short by a fifth. That, then, is called a short bit. If you have one, you lay it triumphantly down, and save two and a half cents. But if you have not, and lay down a quarter, the bar-keeper or shopman calmly tenders you a dime by way of change; and thus you have paid what is called a long bit, and lost two and a half cents, or even, by comparison with a short bit, five cents." Robert Louis Stevenson, Across the Plains, 1892.
The New York Stock Exchange switched from the Spanish system of eighths to the decimal system only 20 years ago, in April 2001.
