To find the area of the pavilion in square feet, we can use the formula:
\[ \text{Area} = \frac{\text{Number of bricks}}{\text{Bricks per square foot}} \]
Given that the total number of bricks is \(2.967 \times 10^5\) and there are \(6.9\) bricks per square foot, we can plug in the values:
\[ \text{Area} = \frac{2.967 \times 10^5}{6.9} \]
Now, we can perform the division:
First, calculate the division of the coefficients:
\[ \frac{2.967}{6.9} \approx 0.4301159420289855 \approx 0.4301 \text{ (keeping four significant figures)} \]
Next, we divide the powers of ten:
Since there is no other power of ten in the denominator, we keep \(10^5\):
\[ \text{Area} \approx 0.4301 \times 10^5 \]
To express this in proper scientific notation, we convert \(0.4301\) into standard scientific notation:
\[ 0.4301 = 4.301 \times 10^{-1} \]
Now we can combine this with \(10^5\):
\[ \text{Area} = 4.301 \times 10^{-1} \times 10^5 = 4.301 \times 10^{4} \]
Thus, the area of the pavilion in square feet is:
\[ \boxed{4.301 \times 10^{4}} \]