1. **State the problem:** We need to find the ratio of the lengths of the purple, green, and orange sections of the pole. 2. **Write down the given lengths:** - Purple = 0.8 m - Green = 1.4 m - Orange = 0.6 m 3. **Form the ratio:** $$\text{Purple} : \text{Green} : \text{Orange} = 0.8 : 1.4 : 0.6$$ 4. **Simplify the ratio:** To simplify, divide each term by the smallest length, which is 0.6: $$\frac{0.8}{0.6} : \frac{1.4}{0.6} : \frac{0.6}{0.6} = \frac{0.8}{0.6} : \frac{1.4}{0.6} : 1$$ 5. **Calculate each fraction:** $$\frac{0.8}{0.6} = \frac{8}{6} = \frac{\cancel{2} \times 4}{\cancel{2} \times 3} = \frac{4}{3}$$ $$\frac{1.4}{0.6} = \frac{14}{6} = \frac{\cancel{2} \times 7}{\cancel{2} \times 3} = \frac{7}{3}$$ 6. **Rewrite the ratio with fractions:** $$\frac{4}{3} : \frac{7}{3} : 1$$ 7. **To express all terms as whole numbers, multiply all parts by 3:** $$3 \times \frac{4}{3} : 3 \times \frac{7}{3} : 3 \times 1 = 4 : 7 : 3$$ 8. **Final answer:** The simplest form of the ratio of purple to green to orange is $$\boxed{4 : 7 : 3}$$