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"Quarter Dollar" and "Five Dollars" and "One Cent" -- the money you carry tells you how much it is worth. But what if the coins only carried an image on both sides with no writing at all? How would you know what it was worth?
In the ancient world, all silver or gold coins were expected to be pure and all coins circulated by weight. Simple balance scales for weighing were common and were fairly accurate. Most people prefered to accept the coins of their own town. But most towns held perhaps only a 1000 people; a city of 10,000 would be a metropolis. So, foreign coins were unavoidable.
Coins from important cities like Athens and Corinth were known by their consistent images. Coins from Athens were called "owls" and the coins of Corinth were called "colts" or "foals." Everyone learned to recognize the coins from the cities of international fame, including Syracuse, Ephesus, and Alexandria.
Also, there were only a few standards at any one time. Important cities like Rhodes and Athens, and the ever-present Phoenician traders, established de facto standards that other people copied. Odd sizes and weights didn't serve anyone's purpose. Sometimes cities worked together to produce a common, federal coinage. Sometimes cities would strike coins that made it easy to buy from the people in other towns.
If you still find this confusing, remember that as computer users, we think nothing of keeping track of a few standard ways to create and write data, sound, or graphics and to combine them into multimedia.