Question

Convert repeating decimal 0.155….to fraction

Answer 1

Given the repeating decimal 0.155...

We will convert it to a fraction as follows:

`\begin{gathered} 0.1555.\ldots=0.1+0.055\ldots \\ \\ =(1)/(10)+(5)/(100-10) \\ \\ =(1)/(10)+(5)/(90)=(9)/(90)+(5)/(90)=(14)/(90)=(7)/(45) \end{gathered}`

so, the answer will be:

`0.1555\ldots=(7)/(45)`