Question

What is the fraction equivalent of the repeating decimal 0.8?

Answer 1

`\begin{gathered} \text{Given} \\ 0.\overline{8}\text{ or }0.888888... \end{gathered}`

Let X be equal to 0.88888....

`X=0.\overline{8}`

With 1 digits in the repeating decimal group, create a second equation by multiplying

both sides by 10

`\begin{gathered} X=0.\overline{8}\text{ \lparen equation 1\rparen} \\ (10)X=(10)0.\overline{8} \\ 10X=8.\overline{8}\text{ \lparen equation 2\rparen} \end{gathered}`

Subtract equation 1, from equation 2

Solve for X

`\begin{gathered} 9X=8 \\ (9X)/(9)=(8)/(9) \\ X=(8)/(9) \\ \\ \text{Therefore, the fraction equivalent of }0.\overline{8}\text{ is }(8)/(9). \end{gathered}`