Question
A rectangular park has an area of 1.36×108 ft2
. The length of the park is 1.6×104
ft. Divide the area by the length to find the width of the park.(1 point)
Responses
8.5×103
ft.
8.5 times 10 cubed ft.
8.5×102
ft.
8.5 times 10 squared ft.
8.5×104
ft.
8.5 times 10 superscript 4 baseline ft.
8.5×105
ft.
8.5 times 10 superscript 5 baseline ft.
. The length of the park is 1.6×104
ft. Divide the area by the length to find the width of the park.(1 point)
Responses
8.5×103
ft.
8.5 times 10 cubed ft.
8.5×102
ft.
8.5 times 10 squared ft.
8.5×104
ft.
8.5 times 10 superscript 4 baseline ft.
8.5×105
ft.
8.5 times 10 superscript 5 baseline ft.
Answers
GPT-4o mini
To find the width of the park, we can use the formula for the area of a rectangle:
\[
\text{Area} = \text{Length} \times \text{Width}
\]
Given the area \( A = 1.36 \times 10^8 \, \text{ft}^2 \) and the length \( L = 1.6 \times 10^4 \, \text{ft} \), we can solve for the width \( W \):
\[
W = \frac{A}{L}
\]
Substituting in the values we have:
\[
W = \frac{1.36 \times 10^8}{1.6 \times 10^4}
\]
To divide these numbers in scientific notation, we can separate the coefficients and the powers of 10:
\[
W = \frac{1.36}{1.6} \times \frac{10^8}{10^4}
\]
Calculating the coefficients:
\[
\frac{1.36}{1.6} = 0.85
\]
Calculating the powers of 10:
\[
\frac{10^8}{10^4} = 10^{8-4} = 10^4
\]
Now we have:
\[
W = 0.85 \times 10^4
\]
To express this in proper scientific notation, we can convert \( 0.85 \) to \( 8.5 \) by moving the decimal one place to the right, which requires reducing the exponent by 1:
\[
W = 8.5 \times 10^{4-1} = 8.5 \times 10^3
\]
Thus, the width of the park is:
\[
\textbf{8.5 × 10³ ft.}
\]
So the correct response is **8.5×10³ ft.**
\[
\text{Area} = \text{Length} \times \text{Width}
\]
Given the area \( A = 1.36 \times 10^8 \, \text{ft}^2 \) and the length \( L = 1.6 \times 10^4 \, \text{ft} \), we can solve for the width \( W \):
\[
W = \frac{A}{L}
\]
Substituting in the values we have:
\[
W = \frac{1.36 \times 10^8}{1.6 \times 10^4}
\]
To divide these numbers in scientific notation, we can separate the coefficients and the powers of 10:
\[
W = \frac{1.36}{1.6} \times \frac{10^8}{10^4}
\]
Calculating the coefficients:
\[
\frac{1.36}{1.6} = 0.85
\]
Calculating the powers of 10:
\[
\frac{10^8}{10^4} = 10^{8-4} = 10^4
\]
Now we have:
\[
W = 0.85 \times 10^4
\]
To express this in proper scientific notation, we can convert \( 0.85 \) to \( 8.5 \) by moving the decimal one place to the right, which requires reducing the exponent by 1:
\[
W = 8.5 \times 10^{4-1} = 8.5 \times 10^3
\]
Thus, the width of the park is:
\[
\textbf{8.5 × 10³ ft.}
\]
So the correct response is **8.5×10³ ft.**