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I assume you mean that it continues indefinitely. ANY number which repeats periodically, ad infinitum, is a rational number. You can convert this one into a fraction (showing that it is a rational number) as follows:Let:

x = 0.135135...

1000x = 135.135135...

Subtract the first equation from the second one. Solving for "x", you get "x" (your original number) as a fraction.

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Yes.

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Q: Is 0.135135135135 rational
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