Divide in Scientific Notation Quick Check

1 of 51 of 5 Items
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.

1 answer

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.