Rewrite as a simplified fraction.
\[\large{0.\overline{7} = {?}}\]

To rewrite \( 0.\overline{7} \) (a repeating decimal) as a simplified fraction, follow these steps:

1. Let \( x = 0.\overline{7} \).

2. Multiply both sides of the equation by 10 to shift the decimal point one place to the right:
   \[ 10x = 7.\overline{7} \]

3. Subtract the original equation \( x = 0.\overline{7} \) from this new equation:
   \[ 10x - x = 7.\overline{7} - 0.\overline{7} \]
   \[ 9x = 7 \]

4. Solve for \( x \):
   \[ x = \frac{7}{9} \]

Thus, \( 0.\overline{7} = \frac{7}{9} \).

Would you like more details or have any questions?

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Here are 5 related questions:

1. How do you convert \( 0.\overline{3} \) into a fraction?
2. What is the decimal form of \( \frac{7}{9} \)?
3. How do you convert a repeating decimal with two digits (e.g., \( 0.\overline{12} \)) into a fraction?
4. What is the difference between terminating and repeating decimals?
5. How can you simplify fractions?

**Tip:** When converting repeating decimals to fractions, multiplying by powers of 10 helps eliminate the repeating part.

Rewrite as a simplified fraction. 0.\overline{7} = {?}

Learn how to convert the repeating decimal 0.\overline{7} into a simplified fraction. This problem involves key algebraic concepts and formulas, perfect for students in Grades 6-8. Follow a step-by-step guide to solve and understand the concept behind decimal to fraction conversion.

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