When the decimal $0.1\overline{2}$ is written as a fraction $\frac{a}{b}$ with $a$ and $b$ being positive integers with a greatest common divisor of $1$, what is $a+b$?
+170 Note that \(0.0\overline2 = \frac2{90}\), and \(0.1=\frac1{10}\), so the decimal is \(\frac2{90} + \frac1{10} = \frac{11}{90}\).
