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 divisor of 1, what is $a+b$?
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
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 divisor of 1, what is $a+b$?
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant

user
556
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 divisor of 1, what is $a+b$?
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