1. **State the problem:** We want to find how many times more bacteria are in a liter of water compared to what a person can see with a microscope. 2. **Given values:** - Number of bacteria in 1 liter of water: $5 \times 10^9$ - Number of bacteria visible to a person: $2 \times 10^2$ 3. **Formula:** To find how many times more bacteria there are, divide the total bacteria by the visible bacteria: $$\text{Times more} = \frac{5 \times 10^9}{2 \times 10^2}$$ 4. **Calculate the division:** $$\frac{5 \times 10^9}{2 \times 10^2} = \frac{5}{2} \times \frac{10^9}{10^2} = 2.5 \times 10^{9-2} = 2.5 \times 10^7$$ 5. **Interpretation:** There are $2.5 \times 10^7$ times more bacteria in a liter of water than what a person can see with a microscope. **Final answer:** $2.5 \times 10^7$