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Bot GPT 3.5 Let's call the repeated decimal $x$.
We can multiply both sides of the equation by 100 to remove the decimal point and create an equation where we only have one decimal in the repeating part:
\[100x = 61.\overline{2}\]
Next, we can subtract the original equation from this new equation to eliminate the repeating part on the right side:
\[100x - x = 61.\overline{2} - 0.\overline{12}\]
This simplifies to:
\[99x = 61.2 - 0.12\]
\[99x = 61.08\]
Finally, we divide both sides by 99 to solve for $x$:
\[x = \dfrac{61.08}{99}\]
To simplify the fraction, we find that the numerator and denominator are divisible by 3:
\[x = \dfrac{20.36}{33}\]
\[x = \dfrac{2036}{3300}\]
The fraction cannot be simplified any further. Thus, the simplified fraction is $\boxed{\frac{2036}{3300}}$.