To find out how many gallons of perfume will be in each container, we can take the total gallons of perfume and divide it by the total number of containers.
First, let's calculate the total number of containers:
\[ 3.5 \times 10^2 = 350 \text{ containers} \]
Next, we'll divide the total gallons of perfume by the number of containers:
\[ \frac{10.5 \text{ gallons}}{350 \text{ containers}} = \frac{10.5}{350} \]
Calculating the division gives us:
\[ \frac{10.5}{350} = 0.03 \]
Now, we need to express 0.03 in scientific notation. The number 0.03 can be written as:
\[ 3.0 \times 10^{-2} \]
However, this specific format doesn't appear in the provided options. Now let's match it with the options given:
- \( 0.35 \times 10^{-1} \) (which equals 0.035)
- \( 0.3 \times 10^{-2} \) (which equals 0.003)
- \( 0.3 \times 10^{-1} \) (which equals 0.03)
- \( 0.3 \times 10^{2} \) (which equals 30)
From the options, the one that equals 0.03 is:
\[ 0.3 \times 10^{-1} \]
Therefore, the answer is:
\[ \boxed{0.3 \times 10^{-1}} \]