1. The problem asks to convert the mixed number $2 \frac{4}{9}$ into a decimal. 2. First, convert the fraction $\frac{4}{9}$ to a decimal. Since $9$ is a denominator that produces a repeating decimal, divide 4 by 9: $$\frac{4}{9} = 0.\overline{4}\overline{4}... = 0.\overline{4}$$ 3. Now add this decimal to the whole number 2: $$2 + 0.\overline{4} = 2.\overline{4}$$ 4. Therefore, the decimal representation of $2 \frac{4}{9}$ is $2.\overline{4}$, which means 2.4444... with 4 repeating infinitely. 5. Among the options given, $2.\overline{4}$ matches the correct decimal form. Final answer: $2.\overline{4}$