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12-66.

Casey wants to know the fractional equivalent of $0.36363636 …$. She writes the number as $0.3 + 0.06 + 0.003 + 0.0006 + …$. She sees that the first term is $0.3$, but she cannot figure out the common ratio. What is Casey’s mistake? Help her solve her problem.

Multiply $N$ by $100$, then subtract $N$.

$100N=36.363636...$

$N=0.363636...$