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"Invented" usually refers to creating a mechanical or electronic device rather than a static item such as a coin.

The 10-cent coin came about as part of a decimal-based currency system suggested by Thomas Jefferson. The original proposal was to have coin denominations in multiples of 10, with "half" values in between. The smallest denomination was to be called a mill, with these ratios:

10 mills = 1 cent

10 cents = 1 dime

10 dimes = 1 dollar

10 dollars = 1 eagle

10 eagles = 1 union

Then there would also be half cents, half dimes, half dollars, etc. As things worked out the mill was too low in value and the union was too high to be useful, but all the other denominations were issued at one time or another, so the dime was simply one of a much larger set of possible coins. Today of course prices are never expressed in dimes. The word "dime" is simply the name of the coin just like nickel or quarter.

Interesting trivia: the coin's original name was "disme", pronounced "DIZ-muh", and based on the French word for one-tenth. That didn't sound right to English-speaking ears and the S was soon dropped.

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