1. **State the problem:** We are given a map distance of 3 cm representing an actual distance of 600 km. We want to find the scale ratio and express it in terms of centimeters. 2. **Understand the scale:** The scale is a ratio comparing the distance on the map to the actual distance. It can be written as $$\text{map distance} : \text{actual distance}$$ 3. **Given:** - Map distance = 3 cm - Actual distance = 600 km 4. **Convert actual distance to centimeters:** Since 1 km = 1000 m and 1 m = 100 cm, $$600\ \text{km} = 600 \times 1000 \times 100 = 60,000,000\ \text{cm}$$ 5. **Write the scale ratio:** $$3\ \text{cm} : 60,000,000\ \text{cm}$$ 6. **Simplify the ratio by dividing both sides by 3:** $$1\ \text{cm} : \frac{60,000,000}{3} = 1\ \text{cm} : 20,000,000$$ 7. **Interpretation:** The scale is 1 : 20,000,000, meaning 1 cm on the map represents 20,000,000 cm in reality. 8. **Check the user's provided scale:** The user wrote 1 : 100,000 which is incorrect for this problem. The correct scale is 1 : 20,000,000. **Final answer:** $$\boxed{1 : 20,000,000}$$