1. **State the problem:** We need to find the sum of the numbers: 22.8, 25.8, 23.5, 20.7, 20.8, 24.7, 27, 22.5, 21, 28.5, 22.6, 24.5, 20.9, 18.9, 16.1, 19.5, 17.8, 22.6, 24.4, 17.6, 21.9, 22.6, 25.1, 18.7, 24.2, 23.1, 18.4, 21.1, 18.6, 18.3, 19.3, 22.8, 18.1, 15.4, 23.6, 21.2, 17.8, 16.8, 20.3, 18.6. 2. **Formula used:** To find the sum of a list of numbers, we use the addition operation: $$\text{Sum} = x_1 + x_2 + x_3 + \cdots + x_n$$ where $x_i$ are the numbers in the list. 3. **Add the numbers step-by-step:** $$22.8 + 25.8 = 48.6$$ $$48.6 + 23.5 = 72.1$$ $$72.1 + 20.7 = 92.8$$ $$92.8 + 20.8 = 113.6$$ $$113.6 + 24.7 = 138.3$$ $$138.3 + 27 = 165.3$$ $$165.3 + 22.5 = 187.8$$ $$187.8 + 21 = 208.8$$ $$208.8 + 28.5 = 237.3$$ $$237.3 + 22.6 = 259.9$$ $$259.9 + 24.5 = 284.4$$ $$284.4 + 20.9 = 305.3$$ $$305.3 + 18.9 = 324.2$$ $$324.2 + 16.1 = 340.3$$ $$340.3 + 19.5 = 359.8$$ $$359.8 + 17.8 = 377.6$$ $$377.6 + 22.6 = 400.2$$ $$400.2 + 24.4 = 424.6$$ $$424.6 + 17.6 = 442.2$$ $$442.2 + 21.9 = 464.1$$ $$464.1 + 22.6 = 486.7$$ $$486.7 + 25.1 = 511.8$$ $$511.8 + 18.7 = 530.5$$ $$530.5 + 24.2 = 554.7$$ $$554.7 + 23.1 = 577.8$$ $$577.8 + 18.4 = 596.2$$ $$596.2 + 21.1 = 617.3$$ $$617.3 + 18.6 = 635.9$$ $$635.9 + 18.3 = 654.2$$ $$654.2 + 19.3 = 673.5$$ $$673.5 + 22.8 = 696.3$$ $$696.3 + 18.1 = 714.4$$ $$714.4 + 15.4 = 729.8$$ $$729.8 + 23.6 = 753.4$$ $$753.4 + 21.2 = 774.6$$ $$774.6 + 17.8 = 792.4$$ $$792.4 + 16.8 = 809.2$$ $$809.2 + 20.3 = 829.5$$ $$829.5 + 18.6 = 848.1$$ 4. **Final answer:** The sum of the numbers is **848.1**. This method ensures accuracy by adding numbers sequentially and checking intermediate sums.