1. The problem is to convert the repeating decimal $76.\overline{2}$ into a fraction. 2. Let $x = 76.2222\ldots$ where the digit 2 repeats infinitely. 3. Multiply $x$ by 10 to shift the decimal point one place: $$10x = 762.2222\ldots$$ 4. Subtract the original $x$ from this equation to eliminate the repeating part: $$10x - x = 762.2222\ldots - 76.2222\ldots$$ 5. This simplifies to: $$9x = 686$$ 6. Solve for $x$: $$x = \frac{686}{9}$$ 7. Convert the improper fraction to a mixed number by dividing 686 by 9: $$686 \div 9 = 76 \text{ remainder } 2$$ 8. So, $$x = 76 \frac{2}{9}$$ 9. Therefore, the repeating decimal $76.\overline{2}$ as a fraction is $76 \frac{2}{9}$. 10. Among the given options, the correct answer is **76 2/9**.