1. **State the problem:** Order the rational numbers 0.40, \frac{3}{7}, 0.4510, and \frac{5}{12} from smallest to largest. 2. **Convert all numbers to decimals for easy comparison:** - 0.40 is already a decimal. - \frac{3}{7} = \frac{3}{7} \approx 0.428571 (dividing 3 by 7). - 0.4510 is already a decimal. - \frac{5}{12} = \frac{5}{12} \approx 0.4166667 (dividing 5 by 12). 3. **List the decimal equivalents:** - 0.40 - 0.428571 - 0.4510 - 0.4166667 4. **Order the decimals from smallest to largest:** - 0.40 - 0.4166667 (\frac{5}{12}) - 0.428571 (\frac{3}{7}) - 0.4510 5. **Write the original numbers in order:** $$0.40 < \frac{5}{12} < \frac{3}{7} < 0.4510$$ **Final answer:** $$\boxed{0.40 < \frac{5}{12} < \frac{3}{7} < 0.4510}$$