To distribute 10.5 gallons of perfume among \( 3.5 \times 10^2 \) containers, we need to divide the total amount of perfume by the number of containers.
First, we'll perform the division:
\[ \text{Gallons per container} = \frac{10.5}{3.5 \times 10^2} \]
We can simplify this calculation step by step:
- Calculate the division of the coefficients:
\[ \frac{10.5}{3.5} = 3 \]
- The denominator includes \( 10^2 \), so we have:
\[ \text{Gallons per container} = \frac{3}{10^2} = 3 \times 10^{-2} \]
Thus, the amount of perfume in each container is:
\[ \boxed{3 \times 10^{-2}} \]
This corresponds to the scientific notation for 0.03 gallons per container.