Yes. It can be written as
111111111111/1000000000, which doesn't simplify. Ugly, but it works.
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111111111111
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.