It is not at all a mystery, so the question is not sensible.
It's not a mystery: a decimal will repeat if the prime factors of the divisor contain any prime except 2 and 5 (the factors of 10, the base of our decimal numbering system).
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terminating decimals repeating decimals
Non-repeating decimals is not a word but a phrase. Non-repeating decimals are irrational numbers.
No, Albert Einstein did not invent repeating decimals.
Terminating and repeating decimals are rational numbers.
Terminating and repeating decimals are.