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?

---

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.