Is 0.135135135135 ... a irrational number?

It is not an irrational number. In this number, the pattern is 135 repeating. Since it repeats in a certain pattern, it is rational.

An irrational number is a number that cannot be written in the form a/b or fractional form

this is repeating so we can just draw a vinculum over the repeting part (135)

it would be represented as

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0.135

this is a rational number