Question
\( \begin{array}{l}\text { Convert Fractions to Repeating Decimals } \\ \text { Convert the following fractions to repeating decimals.. } \\ \frac{2}{11}\end{array}=\begin{aligned} \frac{5}{6} & = \\ \frac{4}{9} & = \\ \frac{2}{3} & = \\ \frac{15}{22} & = \\ \frac{18}{2} & = \\ \frac{13}{11} & = \\ \frac{13}{6} & = \\ \frac{2}{15} & = \\ \frac{2}{99} & =\end{aligned} \)
Ask by Love Dickson. in the United States
Mar 17,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
Here are the fractions converted to repeating decimals:
1. \( \frac{2}{11} = 0.\dot{1}\dot{8} \)
2. \( \frac{5}{6} = 0.8\dot{3} \)
3. \( \frac{4}{9} = 0.\dot{4} \)
4. \( \frac{2}{3} = 0.\dot{6} \)
5. \( \frac{15}{22} = 0.6\dot{8}\dot{1} \)
6. \( \frac{18}{2} = 9 \)
7. \( \frac{13}{11} = 1.\dot{1}\dot{8} \)
8. \( \frac{13}{6} = 2.1\dot{6} \)
9. \( \frac{2}{15} = 0.1\dot{3} \)
10. \( \frac{2}{99} = 0.\dot{0}\dot{2} \)
Solution
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The Deep Dive
To convert fractions to repeating decimals, you can perform long division. For example, dividing 2 by 11 gives you 0.181818..., which is often written as \(0.\overline{18}\). It's that simple! For \( \frac{5}{6} \), carry out the division and you'll find it equals \(0.8333...\) or \(0.\overline{83}\). Likewise, performing similar conversions for the other fractions will yield repeating decimals, making long division a valuable skill in your math toolkit!
