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Solomon needs to distribute 10.5 gallons of perfume among 3.5 times 10^2 containers. How many gallons of perfume will be in each container? Write the answer in scientific notation.

3 times 10^2
3 times 10^-1
0.35 times 10^-1
3 times 10^-2

7 answers

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.

  1. Total amount of perfume: \( 10.5 \) gallons
  2. Number of containers: \( 3.5 \times 10^2 \)

Now, we perform the division:

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

First, simplify \( \frac{10.5}{3.5} \):

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

Now we divide by \( 10^2 \):

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

So the amount of perfume in each container is:

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

Thus, the answer in scientific notation is:

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

A large pavilion is made of 2.967 times 10^5 bricks. There are 6.9 bricks per square foot. How many square feet is the pavilion? Write the answer in scientific notation.
4.3 times 10^5
0.43 times 10^4
2.33 times 10^5
4.3 times 10^4

To find the number of square feet in the pavilion, we need to divide the total number of bricks by the number of bricks per square foot.

  1. Total number of bricks: \( 2.967 \times 10^5 \) bricks
  2. Bricks per square foot: \( 6.9 \)

Now, we perform the division:

\[ \text{Square feet} = \frac{2.967 \times 10^5}{6.9} \]

Calculating \( \frac{2.967}{6.9} \):

\[ \frac{2.967}{6.9} \approx 0.4300 \]

Now, we keep the scientific notation in mind. We can express \( 0.4300 \) as:

\[ 0.4300 = 4.3 \times 10^{-1} \]

However, we have \( 10^5 \) in the numerator, so:

\[ \text{Square feet} = 4.3 \times 10^{-1} \times 10^5 = 4.3 \times 10^{4} \]

Thus, the area of the pavilion in scientific notation is:

\[ \boxed{4.3 \times 10^{4}} \]

10.5 gal / 350 containers = x gallons / 1 container
x = 10.5 gal * 1 container / 350 container = = (10.5/350) = 0.03 = 3*10^-2 gal/container

Let's go through your calculation to confirm the accuracy. We start with the equation:

\[ \frac{10.5 \text{ gal}}{350 \text{ containers}} = \frac{x \text{ gallons}}{1 \text{ container}} \]

To find \( x \), follow these steps:

  1. Rearranging gives:

\[ x = \frac{10.5 \text{ gal} \times 1 \text{ container}}{350 \text{ containers}} \]

  1. Calculate \( \frac{10.5}{350} \):

\[ \frac{10.5}{350} = 0.03 \]

  1. Converting \( 0.03 \) to scientific notation:

\[ 0.03 = 3 \times 10^{-2} \]

So, you are correct:

\[ x = 3 \times 10^{-2} \text{ gallons per container} \]

Thus, each container has \( 3 \times 10^{-2} \) gallons. Thank you for verifying the calculation!

2.967 * 10^5 bricks * (1 ft^2/ 6.9 bricks) = 296700 /6.9 bricks= 43000 ft^2

Let's confirm the calculation step-by-step to find the area in square feet.

You want to calculate the number of square feet in the pavilion using the total number of bricks and the number of bricks per square foot.

  1. You have \( 2.967 \times 10^5 \) bricks.
  2. You know there are \( 6.9 \) bricks per square foot.

The formula to calculate the area in square feet (\( A \)) would be:

\[ A = \frac{2.967 \times 10^5 \text{ bricks}}{6.9 \text{ bricks/ft}^2} \]

Now, let's perform the calculation step-by-step:

Step 1: Calculate the total number of square feet

\[ A = \frac{2.967 \times 10^5}{6.9} \]

Calculating \( \frac{2.967}{6.9} \):

\[ \frac{2.967}{6.9} \approx 0.4300 \]

Step 2: Multiply by \( 10^5 \)

Now multiply this result by \( 10^5 \):

\[ A \approx 0.4300 \times 10^5 \]

Step 3: Convert to scientific notation

Now, convert \( 0.4300 \) into scientific notation:

\[ 0.4300 = 4.3 \times 10^{-1} \] Thus: \[ A \approx 4.3 \times 10^{-1} \times 10^5 = 4.3 \times 10^{4} \text{ ft}^2 \]

So, the area of the pavilion is:

\[ \boxed{4.3 \times 10^{4} \text{ ft}^2} \]

Your initial concept of dividing the number of bricks and converting to square feet is correct, and your final conversion to \( 43,000 \) ft² is correctly represented as \( 4.3 \times 10^4 \) in scientific notation.