How many history (or economics books, for that matter) mention needing exact change on buses?
Or mentions the term/phrase "exact change" at all? If the bus driver (or signage) had said "precise coinage for fare" Kirk and Spock might not have been confused.
Even if you stipulate (which I don't) that there is no money in the Federation, Kirk and his officers must have explored worlds (Gangster, Nazi, Roman, other) where there was a money system. It's fairly ridiculous to assume that they would have absolutely no
experience using physical money. Or be unable to do the simply math of breaking down large denominations of currency, into smaller units.
I can imagine that the Ferengi, a culture steeped in commerce, are incredibly difficult for Starfleet to deal with, simply because they don't trade.
We've seen the 24th century Federation engage in trade, remember the wormhole they were bidding on?
If something hasn't got a moneytary value, the Ferengi aren't interested in it.
Quark was able to sell his damaged shuttle for scrap in the Earth system. And had to pay
for passage back to DS9 from Earth. If he could have traveled for free, I'm sure Quark would have laughed all the way back to the station.
It isn't just the Ferengi who are interested in monetary value.
... it's worth remembering that the old european navies used to establish contact with other countries without currency. They didn't set out with money to convince natives to side with the interests of their home empires, they used trade.
It has to do with exchange rates, and what your customer will accept. It wasn't that long ago in the United States that paper money from one State wouldn't be accepted in another State at face value. The farther you got from home, the less your money was worth. Some small businesses wouldn't take it at all.
So, not just Europeans in the new world.
It wasn't a case of "allow us to use our money which is worthless to you to buy a stake in your country", it was more like "Here are some precious beads from Spain, howsabout we trade them for land in the Mississippi?"
Again it has to do with exchange rates, your money to theirs, you have to remember that particular types of beads (especially blue beads) weren't valueless junk, they were the money of that area of the world (the currency of the realm), because they possessed worth.
If a European trader were to show up with just any kind of beads, the natives would send them on their way with empty hands.
For centuries, Arabs used cowry shells for money. This wasn't because the Arabs were stupid or bad businessmen, it's because these particular shells were the equivalent of gold or jems, they were rare and beautiful.
The Hawaiians used puka shell for money, not because they were laying around everywhere, but because the real ones were rare and valuable. A today a real puka shell can be the equivalent of a five dollar bill.
Beads and shells are
a form of money. This is the shell of a ocean scallop known as Langford's Pecten, it's the size of a American ten cent coin, and is today worth over two hundred dollars.