Repeating decimals are always rational.
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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...
A terminating decimal is a rational number. A non-terminating, repeating decimal is a rational number. A non-terminating, non-repeating decimal is an irrational number.
Any rational number is either a repeating decimal, or a terminating decimal.
It is either a terminating decimal or a repeating decimal.
That is the definition of a rational number.