Q: Is 0.233333... rational

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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.

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Rational. Rational. Rational. Rational.

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No, it is rational.

It is a rational number

It is rational. It is rational. It is rational. It is rational.

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No, it is rational.

It is rational

0.38 is a rational number because it can be expressed as a fraction