Yes, it is.
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Any decimal that terminates or repeats is a rational number; as 0.113113113.... repeats the digits "113" it is a rational number. 0.113113113... = 113/999 (in fraction form).
If you mean to continue the pattern indefinitely, adding more digits, and one more "1" in every cycle, then it is NOT rational. In the case of a rational number, the EXACT SAME group of digits has to repeat over and over (perhaps after some other, initial, digits), for example:0.45113113113113113... Here, the group of digits "113" repeats over and over, so the number is rational.
Is 12.05 a rational number or irrational number?
1.96 is a rational number
There is no such thing as a number that is both rational and irrational. By definition, every number is either rational or irrational.