1. **State the problem:** We need to find the ratio of the lengths of the purple, green, and orange sections of the pole. 2. **Given lengths:** - Purple = 0.8 m - Green = 1.4 m - Orange = 0.6 m 3. **Write the ratio:** $$\text{Purple : Green : Orange} = 0.8 : 1.4 : 0.6$$ 4. **Simplify the ratio:** To simplify, divide each term by the smallest length, which is 0.6: $$\frac{0.8}{0.6} : \frac{1.4}{0.6} : \frac{0.6}{0.6} = \frac{8}{6} : \frac{14}{6} : 1$$ 5. **Convert to whole numbers:** Multiply each term by 3 to clear denominators: $$\frac{8}{6} \times 3 : \frac{14}{6} \times 3 : 1 \times 3 = 4 : 7 : 3$$ 6. **Final answer:** The simplest form of the ratio of purple to green to orange is: $$\boxed{4 : 7 : 3}$$