1. **State the problem:** Carrie eats 2 whole satsumas and then eats 1 segment out of 8 equal segments of another satsuma. We need to find the total satsumas eaten as an improper fraction in simplest form. 2. **Write the total satsumas eaten:** $$2 + \frac{1}{8}$$ 3. **Convert the whole number to a fraction with denominator 8:** $$2 = \frac{2 \times 8}{8} = \frac{16}{8}$$ 4. **Add the fractions:** $$\frac{16}{8} + \frac{1}{8} = \frac{16 + 1}{8} = \frac{17}{8}$$ 5. **Simplify the fraction:** The fraction $$\frac{17}{8}$$ is already in simplest form because 17 is a prime number and does not share any common factors with 8. **Final answer:** $$\boxed{\frac{17}{8}}$$