1. Stating the problem: Convert the decimal number 9.519 into a simplified mixed fraction. 2. Separate the integer and decimal parts: The integer part is 9 and the decimal part is 0.519. 3. Convert the decimal part 0.519 into a fraction: Since 0.519 has three decimal places, write it as $$\frac{519}{1000}$$. 4. Simplify the fraction $$\frac{519}{1000}$$: Factor numerator and denominator to find the greatest common divisor (GCD). - Prime factors of 519: 3 \times 173 - Prime factors of 1000: 2^3 \times 5^3 GCD is 1 because numerator and denominator share no common prime factors. Therefore, $$\frac{519}{1000}$$ is already in simplest form. 5. Write the mixed number: The mixed number is $$9 \frac{519}{1000}$$. Final Answer: $$9 \frac{519}{1000}$$