98.5k views
3 votes
Express the repeating decimal 0.2 as a fraction

User TBB
by
8.2k points

1 Answer

5 votes

Answer:

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)

User Andycam
by
8.5k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories