At 9:38 A.M, through how many degrees the hour hand of a clock moved since noon the previous day?

### Concept & Long-duration Hour Hand Movement To find the total degrees covered by an hour hand over a long period, find the total elapsed time in minutes and multiply by the hour hand's speed ($0.5°$ per minute). ### Step-by-Step Solution 1. **Given:** Start time = 12:00 Noon (previous day). End time = 9:38 A.M (current day). 2. Calculate elapsed time: Noon to Midnight = 12 hours. Midnight to 9:38 A.M = 9 hours 38 minutes. Total elapsed time = 21 hours 38 minutes. 3. Convert the total time to minutes: $$21 \text{ hours} = 21 \times 60 = 1260 \text{ minutes}$$ Total minutes = $1260 + 38 = 1298 \text{ minutes}$. 4. The hour hand moves at $0.5°$ per minute. Multiply total minutes by $0.5$: $$\text{Total degrees} = 1298 \times \frac{1}{2} = 649°$$ ### Exam Strategy & Shortcut Break the calculation into chunks based on rotations. 12 hours = $360°$. 9 hours = $9 \times 30° = 270°$. 38 minutes = $38 \times 0.5° = 19°$. Total = $360° + 270° + 19° = 649°$. ### Common Pitfall Miscounting the hours between noon and 9:38 AM the next day. Sometimes students count 24 hours minus the difference, making simple subtraction errors across the day boundary. ### Final Answer Therefore, the correct answer is **649**.