Solomon needs to distribute 10.5 gallons of perfume among 3.5×10^2

Question

3.5
×
10
2
containers. How many gallons of perfume will be in each container? Write the answer in scientific notation.(1 point)
Responses

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

3×10^2
3
×
10
2
3 times 10 squared

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

3×10^−2

Answer 1

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:

1. Calculate the division of the coefficients:

\[ \frac{10.5}{3.5} = 3 \]

2. 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.