Question

Divide in Scientific Notation Quick Check
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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.

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

8.5×105 ft.
8.5 times 10 superscript 5 baseline ft.

8.5×102 ft.

Answer 1

To find the width of the park, you can divide the area by the length using scientific notation.

Given:
- Area = \( 1.36 \times 10^8 \) ft²
- Length = \( 1.6 \times 10^4 \) ft

We can set up the division as follows:

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

To simplify this division, we will divide the coefficients and subtract the exponents of the powers of 10:

1. Divide the coefficients:
\[
\frac{1.36}{1.6} = 0.85
\]

2. Subtract the exponents:
\[
10^{8 - 4} = 10^4
\]

Now, combine the results:
\[
\text{Width} = 0.85 \times 10^4
\]

To express it in proper scientific notation, we adjust \(0.85\) to \(8.5\) by reducing the exponent on the \(10\):
\[
0.85 \times 10^4 = 8.5 \times 10^{3}
\]

Thus, the width of the park is \(8.5 \times 10^3\) ft.

The correct response is:
**8.5×10³ ft.**