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## Friday, March 9th, 2012

### Large Numbers

Categories: [ Science ] My daughter asked me yesterday what is the largest number I know. The answer was “a Googolplex”, which is 10googol with googol = 10100.

While you can write a googol on a sheet of paper (it's a one followed by 100 zeros), you cannot write a googolplex on paper. Or can you? how much paper do you need for that?

Let's assume you can write 10 000 digits on one sheet of A4 paper. You therefore need 1096 sheets of paper. One tree can produce 10 000 sheets of paper, and there are about 1012 trees on Earth. You'd need 1080 Earths to provide all the paper. Not going to work.

Now let's see if there's even enough matter in the universe to make all this paper: assuming that all the matter in the universe can be converted to paper, is there enough of it? Paper is made of cellulose, chains of D-glucose, the latter weighing 128 g/mol. So a 5 g sheet of A4 paper contains about 2.5·1022 molecules of linked D-glucose, each of which is made of 128 hadrons (protons and neutrons). A sheet of paper is therefore made of 3·1024 hadrons, which is almos the same thing as an atom of hydrogen. The universe contains roughly 1080 atoms, which translate roughly as 1056 sheets of paper. We'd need 1040 universes to make all the needed paper. Not going to work either.

That was a very big number.

[ Posted on March 9th, 2012 at 11:44 | 1 comment | ]