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Yes, there were many dollar coins with errors. One of the best known dollar error coin was the Sacagawea dollar coin and Washington quarter mule error. Only 12 of these coins were made and they can be up to $100,000.
The number 51.2 is known as a decimal. The decimal is in the 10th place.
The collection and/or study of coins is called Numismatics.
No.
A terminating decimal or a decimal that, after a finite number of digits, settles into a repeating pattern (known as a recurring decimal). This need not happen straight after the decimal point.