68.0k views
3 votes
Convert 0.111... to a repeating fraction. simplify if you can

1 Answer

4 votes

Step-by-step explanation:

To convert from a repeating decimal number to a fraction we have to do the following steps:

1. Let 'x' be the repeating decimal:


x=0.111\ldots

2. Let 'n' be the number of decimals that repeat. In this case n = 1

3. Multiply both sides of point 1 by 10^n:


10x=1.111\ldots

4. Substract (1) from (3) to eliminate the repeating part:


\begin{gathered} 10x-x=1.111\ldots-0.111\ldots \\ 9x=1 \end{gathered}

5. Solve for x:


\begin{gathered} 9x=1 \\ x=(1)/(9) \end{gathered}

6. Simplify: in this case, it is the simplest form for this fraction

Answer:

0.111... as a fraction is 1/9

User Rob Allen
by
8.0k 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