To find out how many gallons of perfume will be in each container, we need to divide the total amount of perfume by the number of containers.
Solomon has 10.5 gallons of perfume and 3.5 × 10² containers.
First, we can convert 10.5 into scientific notation: 10.5 = 1.05 × 10¹
Next, we set up the division: \[ \frac{1.05 \times 10^1}{3.5 \times 10^2} \]
We can simplify this division in two steps:
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Divide the coefficients: \[ \frac{1.05}{3.5} = 0.3 \]
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Divide the powers of ten using the rule \( \frac{10^m}{10^n}=10^{m-n} \): \[ \frac{10^1}{10^2} = 10^{1-2} = 10^{-1} \]
Now we can combine the results: \[ 0.3 \times 10^{-1} \]
Next, we need to convert \(0.3\) into scientific notation: \[ 0.3 = 3.0 \times 10^{-1} \]
Now combine this with \(10^{-1}\): \[ 3.0 \times 10^{-1} \times 10^{-1} = 3.0 \times 10^{-2} \]
Thus, the amount of perfume in each container, in scientific notation, is:
\[ 3 \times 10^{-2} \]
The correct response is: 3×10−2 (3 times 10 negative squared).