1 year ago
Last edited at 12:45AM on 6/22/2012
The key point is that you don't need to count: you can easily get an order of magnitude estimate, and be wrong by a factor of perhaps a few if you treat it as a Fermi problem. So here is how I estimate it:
The area of the Sahara desert (from Wikipedia) is 9.4x10^6 sq. km, or 10^7 sq. km = 10^13 m^2.
The average depth of sand: couldn't readily find it, so I estimate as 5 m. That's because there are very deep dunes, but also rocky areas, so 5m sounds not unreasonable.
The volume of sand is therefore 5x10^13 m^3.
The volume of a grain of sand is tricky: they come in many different sizes, spanning 6 orders of magnitude. A large grain of sand is 10^(-9) m^3, and a small one is 10^(-12) m^3. Let's assume the average sand grain in the Sahara is a medium one, whose volume is 10^(-12) m^3.
Dividing the two volumes, the number of grains of sand in the Sahara is 5x10^13/10^(-12) ~ 5x10^(25). The factor of 5 can of course be dropped.
So the answer is 10^(25), or 1 with 25 zeros after it.