Just a drop in the bucket

If approximately 70%70 \% 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 2478=2.478×1032478 = 2.478 \times 10^{3} is 33.

Details and assumptions

  • The earth's radius is 6380 km6380~\mbox{km}.
  • The radius of a raindrop is 1 mm1~\mbox{mm}; raindrops can be approximated to be spherical.
  • The average ocean depth is 2 km2~\mbox{km}.

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