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

8.5×104
ft.
8.5 times 10 superscript 4 baseline ft.

8.5×103
ft.
8.5 times 10 cubed ft.

8.5×102
ft.
8.5 times 10 squared ft.

8.5×105
ft.

Answer 1

To find the width of the park, we can use the formula for the area of a rectangle, which is:

\[
\text{Area} = \text{Length} \times \text{Width}
\]

We can rearrange this to find the width:

\[
\text{Width} = \frac{\text{Area}}{\text{Length}}
\]

Given:

- Area = \( 1.36 \times 10^8 \, \text{ft}^2 \)
- Length = \( 1.6 \times 10^4 \, \text{ft} \)

Now we can substitute these values into the formula for width:

\[
\text{Width} = \frac{1.36 \times 10^8}{1.6 \times 10^4}
\]

To divide the numbers, we first divide the coefficients:

\[
\frac{1.36}{1.6} = 0.85
\]

Next, we divide the powers of ten:

\[
\frac{10^8}{10^4} = 10^{8-4} = 10^4
\]

Now we can combine the results:

\[
\text{Width} = 0.85 \times 10^4
\]

To convert \( 0.85 \times 10^4 \) into scientific notation, we can write it as:

\[
8.5 \times 10^3 \quad \text{(since } 0.85 = 8.5 \times 0.1 \text{ and moving the decimal point one place to the right increases the exponent by 1)}
\]

Thus, the width of the park is:

\[
\text{Width} = 8.5 \times 10^3 \, \text{ft}
\]

Therefore, the correct response is:

**8.5×10³ ft.**