Solomon needs to distribute 10.5 gallons of perfume among 3.5×10^2 containers. How many gallons of perfume will be in each container? Write the answer in scientific notation.(1 point)
Responses
3×102
3 times 10 squared
0.35×10−1
0.35 times 10 superscript negative 1 baseline
3×10−2
3 times 10 negative squared
3×10^−1
The correct answer is 3×10^−1 gallons of perfume in each container.
To find the number of gallons of perfume in each container, we need to divide the total gallons (10.5) by the number of containers (3.5×10^2).
10.5 / (3.5×10^2)
To divide by a number in scientific notation, we divide the numbers and subtract the exponents:
10.5 / 3.5 = 3
10^2 / 10^2 = 1
So, the answer is 3 times 10 squared, or 3×10^2.
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 (3.5×10^2).
The formula to calculate this is:
(gallons of perfume) / (number of containers) = (gallons of perfume per container)
Plugging in the values from the question:
10.5 gallons / 3.5×10^2 containers = (10.5 / 3.5) × (1 / 10^2) gallons
Simplifying this calculation:
= 3 gallons × 10^-2 gallons
To write the answer in scientific notation, we represent 3 as 3×10^0 and 10^-2 as 1/10^2 or 10^-2. Combining these:
= 3×10^0 × 10^-2 gallons
Using the rule of multiplying variables with the same base (10 in this case), we add the exponents:
= 3×10^(0-2) gallons
= 3×10^-2 gallons
Therefore, the answer in scientific notation is 3×10^-2 gallons.