1. **State the problem:** Find how many numbers between 10 and 200 are exactly divisible by 7. 2. **Formula and rules:** A number is divisible by 7 if it can be written as $7k$ where $k$ is an integer. 3. **Find the smallest multiple of 7 greater than 10:** $$\text{Smallest } = 7 \times \lceil \frac{10}{7} \rceil = 7 \times 2 = 14$$ 4. **Find the largest multiple of 7 less than or equal to 200:** $$\text{Largest } = 7 \times \lfloor \frac{200}{7} \rfloor = 7 \times 28 = 196$$ 5. **Count the multiples between 14 and 196:** The multiples are $7 \times 2, 7 \times 3, ..., 7 \times 28$. Number of multiples = $28 - 2 + 1 = 27$ **Final answer:** There are **27** numbers between 10 and 200 exactly divisible by 7.