Divide in Scientific Notation Quick Check

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Question
Solomon needs to distribute 10.5 gallons of perfume among 3.5×102
containers. How many gallons of perfume will be in each container? Write the answer in scientific notation.(1 point)
Responses

3×102
3 times 10 squared

3×10−2
3 times 10 negative squared

3×10−1
3 times 10 superscript negative 1 baseline

0.35×10−1
0.35 times 10 superscript negative 1 baseline
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1 answer

To find out how many gallons of perfume will be in each container, we will divide the total amount of perfume by the number of containers.

Given:

  • Total perfume = \( 10.5 \) gallons
  • Number of containers = \( 3.5 \times 10^2 \)

We perform the calculation as follows:

\[ \text{Gallons per container} = \frac{10.5}{3.5 \times 10^2} \]

To simplify \( \frac{10.5}{3.5} \): \[ \frac{10.5}{3.5} = 3 \]

Now to calculate: \[ \text{Gallons per container} = \frac{3}{10^2} = 3 \times 10^{-2} \]

So, the number of gallons of perfume in each container is:

\[ 3 \times 10^{-2} \]

Thus, the correct response is:

3×10−2 (3 times 10 to the negative 2)