Why does money need to be divisible?
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Money needs to be divisible so that it can effectively act as a medium of exchange. If money is not divisible, it becomes hard to buy small items and it becomes difficult to have precise pricing.
Imagine, for example, if we tried to use cattle as money. This would be a big problem because there are surely many things that are not worth a whole cow. If you wanted to buy a movie ticket, for example, what you do? You couldn't cut off some percentage of the cow and give it to the ticket taker. If money is going to be useful, it has to be divisible so we can buy small things and so we can have precise prices (imagine trying to distinguish between something that cost $2 and something that cost $2.50 if you were using cattle as money...).
For anything to act as the medium of exchange it should be available in a wide range of values so that all items, whether very expensive or extremely cheap, can be bought and sold. It is for this very reason that money should be divisible.
In US, the smallest possible unit of available money is 1 penny and it is available in multiples of penny (5, 10, 25, 100, 500, etc.). This enables buying something as cheap as a candy and as expensive as a house or ship.
Divisibility of currency is also the reason why metals such as, gold, silver, bronze (not a metal, but an alloy of metals), etc. were so commonly used in human history as the currency. Compare this to the barter system, where live animals were used instead of money. How would you buy an item that is not worth an entire animal. Say 10 kg of grain is worth 1 sheep, but how do you pay for a candy: with a small piece of sheep.
Thus, we have a system of money/currency that is divisible into smaller units.
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