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 0.35×10−1 0.35 times 10 superscript negative 1 baseline 3×102 3 times 10 squared 3×10−2 3 times 10 negative squared 3×10−

Answer 1

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 × 10²).

1. Calculate the number of containers: \[ 3.5 \times 10^2 = 3.5 \times 100 = 350 \]

2. Now, divide the total amount of perfume by the number of containers: \[ \frac{10.5}{350} \]

3. To simplify this division, convert 10.5 to a fraction: \[ 10.5 = \frac{105}{10} = \frac{105 \div 5}{10 \div 5} = \frac{21}{2} \]

4. Thus: \[ \frac{21/2}{350} = \frac{21}{2} \times \frac{1}{350} = \frac{21}{700} = \frac{3}{100} = 0.03 \]

5. Now, write this in scientific notation: \[ 0.03 = 3 \times 10^{-2} \]

Thus, the answer is \( 3 \times 10^{-2} \).