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We construct a number $\alpha$ in decimal by the following rules:

Rule 1: The number $\alpha$ starts with the first digit $0$, i. e. its decimal expansion is $0. ***\cdots $.

Rule 2: The $n$-th digit of $\alpha$ after the decimal point is $0$ if $n$ is not a prime, and it is $1$ if $n$ is a prime.

Which of the following statement is true? Select ONE answer.


$\alpha$ is rational.


$\alpha$ is irrational.


It is impossible to determine that $\alpha$ is rational or irrational.

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