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# When the decimal $0.1\overline{23}$ is written as a fraction $\frac{a}{b}$ with $a$ and $b$ being positive integers with a greatest common d

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When the decimal  is written as a fraction  with  and  being positive integers with a greatest common divisor of 1, what is ?

Jul 21, 2019

$$0.1\overline{23}$$ is the same thing as 122/990. Since they have to have a GCD of 1, we must simplify them, where we get 61/495. Now we add the numerator and denominator getting $$61+495 = \boxed{556}$$