1. The problem is to simplify the fraction $\frac{4}{9}$ and express it as a decimal. 2. To convert a fraction to a decimal, divide the numerator by the denominator. 3. Perform the division: $$\frac{4}{9} = 4 \div 9$$ 4. Since 4 is less than 9, the decimal will be less than 1. We add a decimal point and zeros to continue the division. 5. Divide 40 by 9: $$9 \times 4 = 36$$, remainder 4. 6. Bring down another 0, divide 40 by 9 again: remainder 4. 7. This process repeats, so the decimal is repeating: $$0.\overline{4}$$ 8. Therefore, the decimal equivalent of $\frac{4}{9}$ is $0.\overline{4}$, which is approximately $0.4444$. Final answer: $0.\overline{4}$