### Instruction: The number 4 is written on my whiteboard. Every time it rains, I multiply the number on the whiteboard by $\frac{2}{3}$, erase the original number, and write the new number on the whiteboard. When it snows, I multiply the number on the whiteboard by $\frac{3}{5}$, and I replace the original number with the new number. It has rained 5 times and snowed 4 times this month. At the end of the month, what number is on the whiteboard?### Response: To find the final number, I need to keep track of how the number changes after each rain or snow event.
I can use a table to organize the information.
I'll start with 4 in the first row and then apply the appropriate multiplier for each subsequent row.
| Event | Number | Multiplier |
|-------|--------|------------|
| Start | 4      |            |
| Rain  | 2.67   | 2/3        |
| Snow  | 1.60   | 3/5        |
| Rain  | 1.07   | 2/3        |
| Snow  | 0.64   | 3/5        |
| Rain  | 0.43   | 2/3        |
| Snow  | 0.26   | 3/5        |
| Rain  | 0.17   | 2/3        |
| Snow  | 0.10   | 3/5        |
| Rain  | 0.07   | 2/3        |
The final number on the whiteboard is 0.07.