The rate of motion of the earth at its equator is about 1,038 mi/h because of its rotation. From this information, estimate the earth's circumference using an order-of-magnitude estimate.

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To estimate the Earth's circumference using an order-of-magnitude estimate, we can approximate the speed of the Earth at its equator and then use this information to calculate the circumference.

Given that the rate of motion of the Earth at its equator is approximately 1,038 mi/h, we can use this value to estimate the distance traveled by the Earth in one hour.

Since the Earth takes 24 hours to complete one full rotation, we can assume that in one hour, it covers approximately 1/24th of its circumference.

Therefore, the distance covered by the Earth in one hour is roughly 1/24th of the circumference.

Calculating the estimated circumference:
Circumference = Distance covered in one hour × 24

Substituting the given rate of motion:
Circumference ≈ 1,038 mi/h × 24

Now, we can calculate the approximate value of the Earth's circumference using this equation.

Circumference ≈ 24,912 miles

Hence, using an order-of-magnitude estimate, the Earth's circumference is estimated to be approximately 24,912 miles.