Question

Express the repeating decimal 0.2 as a fraction

Answer 1

The fraction form of the repeating decimal is;

`(2)/(9)`

Step-by-step explanation:

We want to express the repeating decimal 0.2 (2 repeating) as a fraction.

let x represent the fraction;

`\begin{gathered} x=0.2222\ldots \\ 10x=2.222\ldots \end{gathered}`

Then subtract x from 10x;

`\begin{gathered} 10x-x=2.222\ldots-0.222\ldots \\ 9x=2.0 \end{gathered}`

Then we can divide both sides by the coefficient of x;

`\begin{gathered} (9x)/(9)=(2)/(9) \\ x=(2)/(9) \end{gathered}`

Therefore, the fraction form of the repeating decimal is;

`(2)/(9)`