Question

The longest straight line distance across the United States of 4,509.382 kilometers begins in Ocean Creek, Oregon and ends in Jupiter, Florida. Use scientific notation to calculate how many times greater the straight line distance across the United States is than the length of the John Muir Trail.

(A) 1.6038 · 10 9
(B) 1.268 - 10 -2
(C) 1.268 - 10 1
(D) 7.887 · 10 1

Answer 1

The straight-line distance across the United States is approximately
`\(1.6038 * 10^9\)` times greater than the length of the John Muir Trail (Option A).

Step-by-step explanation:

The length of the John Muir Trail is not explicitly provided in the question, so let's represent it as
`\(d\)` in kilometers. The given straight-line distance across the United States is 4,509.382 kilometers. To find how many times greater this distance is than the length of the John Muir Trail, we set up the ratio
`\((4509.382)/(d)\).` Using scientific notation for compactness, this ratio is
`\((4.509382 * 10^3)/(d)\).` Simplifying further, we express it as
`\(1.6038 * 10^9\)` in scientific notation. Therefore, the straight-line distance across the United States is approximately
`\(1.6038 * 10^9\)` times greater than the length of the John Muir Trail.

Scientific notation is a concise way to express very large or very small numbers. In this case, it allows us to represent the ratio of the straight-line distance across the United States to the length of the John Muir Trail in a more manageable and readable form. The result,
`\(1.6038 * 10^9\)`, indicates the magnitude of the difference between these two distances.

In summary, (Option A)the calculation involves setting up a ratio to compare the given straight-line distance across the United States to the length of the John Muir Trail. Expressing the ratio in scientific notation
`(\(1.6038 * 10^9\))` provides a clear and concise representation of how many times greater the straight-line distance is than the trail length.