1. The problem is to convert a recurring decimal into a fraction. 2. Let's consider the recurring decimal $x = 0.\overline{3}$, which means the digit 3 repeats indefinitely. 3. To convert this to a fraction, we use the formula for recurring decimals: If $x = 0.\overline{a}$ where $a$ is a single repeating digit, then $x = \frac{a}{9}$. 4. For $x = 0.\overline{3}$, the repeating digit $a = 3$, so: $$x = \frac{3}{9}$$ 5. Simplify the fraction by dividing numerator and denominator by their greatest common divisor (3): $$x = \frac{3 \div 3}{9 \div 3} = \frac{1}{3}$$ 6. Therefore, the recurring decimal $0.\overline{3}$ equals the fraction $\frac{1}{3}$. This method works similarly for other recurring decimals with one repeating digit.