If approximately of the Earth's surface is covered with water, what is the order of magnitude for the number of raindrops in the world's oceans?
Hint: The order of magnitude of is .
Details and assumptions
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We should first calculate the volume of the ocean: V = 0 . 7 × 4 π R 2 d (a more correct formula would be 0 . 7 × 3 4 π ( R 3 − ( R − d ) 3 ) but we do not need this kind of precision since we are trying to find the order of magnitude). On the other hand, that volume should be made out of raindrops: N 3 4 r 3 π , where N is the number of raindrops. Expressing N from these equations we get N = 1 . 7 0 9 6 × 1 0 2 6 , which has the order of magnitude 2 6 .