I came across this question: "Is the decimal $0.1....1$ with $1$ in every $10^i$ an irrational or a rational number?" and I am trying to figure it out, but I don't know where to start. The numbers I construct are $0.1 \cdots 1 \cdots 1$ with one in the first position (the only exception to the $10^i$th rule) , then the 10th, then the 100th, and so on... I am not sure this constitutes a "pattern", such that the number is considered rational but I am not sure I am right. Beginning with the definition if it is rational, it should be able to be written as $p \over q$. I also thought of multiplying many times with $10^i$ but I don't get anywhere with that idea. Any hints on how to approach this?
2026-04-02 10:33:02.1775125982
Is the decimal $0.1....1$ with $1$ in every $10^i$ an irrational or a rational number?
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