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The problem asks to rewrite \( 0.\overline{8} \) (a repeating decimal) as a simplified fraction.

Let \( x = 0.\overline{8} \). This means that:

\[
x = 0.88888\ldots
\]

To convert this repeating decimal into a fraction:

1. Multiply both sides by 10 to shift the decimal point:
   \[
   10x = 8.88888\ldots
   \]

2. Subtract the original equation \( x = 0.88888\ldots \) from this new equation:
   \[
   10x - x = 8.88888\ldots - 0.88888\ldots
   \]

3. This simplifies to:
   \[
   9x = 8
   \]

4. Solve for \( x \):
   \[
   x = \frac{8}{9}
   \]

Thus, \( 0.\overline{8} \) is equal to \( \frac{8}{9} \) in fraction form.

Would you like more details or have any questions?

Here are 5 related questions to practice:
1. Convert \( 0.\overline{7} \) into a fraction.
2. Express \( 0.\overline{5} \) as a fraction.
3. How do you convert \( 0.\overline{23} \) into a fraction?
4. What is \( 0.\overline{9} \) as a simplified fraction?
5. Can every repeating decimal be written as a fraction? Why?

**Tip**: To convert repeating decimals into fractions, shift the decimal point using multiplication, subtract to eliminate the repeating part, and then solve for the variable.

Rewrite as a simplified fraction: 0.8 (with repeating decimal bar) = ?

Learn how to convert the repeating decimal 0.8 (with a repeating bar) into a simplified fraction using algebraic techniques. Suitable for students in Grades 7-9, this explanation breaks down the process with formulas and examples.

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