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Repeating decimals are always rational.
They can. And if you include repeating 0s and repeating 9s, then all rational numbers can be written with infinitely long repeating digits.
Yes, a rational number can be a repeating decimal. A repeating decimal is a decimal in which one or more digits repeat infinitely. For example, 1/3 is a rational number that can be written as the repeating decimal 0.333...
Any time your decimal is not repeating, it is rational.
Any rational number is either a repeating decimal, or a terminating decimal.