To find out how many gallons of perfume will be in each container, we need to divide the total amount of perfume (10.5 gallons) by the number of containers (3.5 x 10^2).
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First, convert the total number of containers into a numerical value: \[ 3.5 \times 10^2 = 3.5 \times 100 = 350 \text{ containers} \]
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Now divide the total gallons of perfume by the number of containers: \[ \text{Gallons per container} = \frac{10.5}{350} \]
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Performing the division: \[ \frac{10.5}{350} = 0.03 \]
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Now, we need to convert 0.03 into scientific notation. In scientific notation, 0.03 can be expressed as: \[ 3.0 \times 10^{-2} \]
Thus, the amount of perfume in each container is \( \boxed{3.0 \times 10^{-2}} \) gallons.