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The repeating decimal \(0.\overline{5}\) is equivalent to a fraction. To convert a repeating decimal to a fraction, follow these steps:

1. Let \( x = 0.\overline{5} \).
2. Multiply both sides by 10 to shift the decimal point: 
   \[
   10x = 5.\overline{5}
   \]
3. Subtract the original equation from this new equation:
   \[
   10x - x = 5.\overline{5} - 0.\overline{5}
   \]
   This simplifies to:
   \[
   9x = 5
   \]
4. Solve for \( x \):
   \[
   x = \frac{5}{9}
   \]

Thus, \( 0.\overline{5} \) is equivalent to the fraction \( \frac{5}{9} \).

Let me know if you need more details or have any questions! 

Here are 5 related questions:
1. How do you convert other repeating decimals into fractions?
2. What is the process for converting non-repeating decimals into fractions?
3. Can \(0.\overline{5}\) be simplified further in any way?
4. How do you find the decimal representation of fractions like \( \frac{7}{9} \)?
5. How do mixed repeating decimals, such as \(0.3\overline{4}\), convert into fractions?

**Tip:** When converting repeating decimals to fractions, it's helpful to use algebraic manipulation to eliminate the repeating part.

What fraction is equivalent to 0.\overline{5}?

Learn how to convert the repeating decimal 0.5 to a fraction using algebraic methods. This problem involves basic algebra and demonstrates the conversion process, arriving at the fraction 5/9. Suitable for students in Grades 6-8.

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