Given the repeating decimal 0.155...
We will convert it to a fraction as follows:
[tex]\begin{gathered} 0.1555.\ldots=0.1+0.055\ldots \\ \\ =\frac{1}{10}+\frac{5}{100-10} \\ \\ =\frac{1}{10}+\frac{5}{90}=\frac{9}{90}+\frac{5}{90}=\frac{14}{90}=\frac{7}{45} \end{gathered}[/tex]so, the answer will be:
[tex]0.1555\ldots=\frac{7}{45}[/tex]