Yes, the number 0.3636363636 is rational because it can be expressed as a fraction. Specifically, it is a repeating decimal that can be written as ( \frac{36}{99} ) or simplified to ( \frac{4}{11} ). Rational numbers are defined as numbers that can be expressed as the quotient of two integers, which applies in this case.
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No, it is rational.
It is rational. It is rational. It is rational. It is rational.
"Rational" is an adjective and so there cannot be "a rational" (and certainly not "an rational"). Any answer would depend on whether the question was about a rational number, a rational person, a rational argument or "a rational" combined with some other noun.
It is rational.
It is rational.