A large pavilion is made of 2.967×10^5 bricks. There are 6.9 bricks per square foot. How many square feet is the pavilion? Write the answer in scientific notation.(1 point)

Question

Responses

4.3×105
4.3 times 10 superscript 5 baseline

0.43×104
0.43 times 10 superscript 4 baseline

4.3×104
4.3 times 10 superscript 4 baseline

2.33×10^5

Answer 1

To find the number of square feet in the pavilion, we can use the relationship given:

\[ \text{Number of bricks} = \text{Bricks per square foot} \times \text{Square feet} \]

We can rearrange this formula to solve for square feet:

\[ \text{Square feet} = \frac{\text{Number of bricks}}{\text{Bricks per square foot}} \]

Substituting the values we have:

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

Now, performing the division:

1. Calculate the coefficient: \[ \frac{2.967}{6.9} \approx 0.4303 \]

2. The power of ten remains the same: \[ 10^5 \]

So we have:

\[ \text{Square feet} \approx 0.4303 \times 10^5 \]

Now we convert \(0.4303\) to scientific notation. This is done by moving the decimal place one position to the right (which increases the exponent by one):

\[ 0.4303 \times 10^5 = 4.303 \times 10^4 \]

Since we need to express this in the form of scientific notation suitable for the answer options, we can round \(4.303\) to \(4.3\) for simplicity:

\[ \text{Square feet} \approx 4.3 \times 10^4 \]

Thus, the final answer is:

\(\boxed{4.3 \times 10^4}\)