Yes.
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Is 0.88 repeating a rational number
It is a rational number.
Any repeating decimal digits (this includes repetition after a certain point, e.g. 2.4510101010...) is a rational number.
Yes, 5.5 repeating, also written as 5.555..., is a rational number. A rational number is any number that can be expressed as a fraction where the numerator and denominator are integers. In this case, 5.5 repeating can be written as 11/2, which is a fraction with integer numerator and denominator, making it a rational number.
Yes.