How big is googol?

Josh Kerr -

Googol is a big number. The search engine was famously named after it. There are several ways that we can think about Googol. Written with exponents, the number can be represented like so:

$$ 10^{100} $$

If you expand it out you would write a 1 followed by 100 zeros:

10000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000

That looks big, but how big is it really? Quite big. Googol is bigger than the number of elementary particles in the Universe. That number is estimated to be \(10^{80}\). Another way to think about the size of google is to take a fish tank the size of the Universe. That fish tank would be 46 billion light years cubed. Now fill it with sand and then count the grains. The count would be 10x less than a Googol.

Some other ways to think about how big Googol is:

  1. The decay time for a supermassive black hole of roughly \(10^{11}\) solar masses in size due to Hawking Radiation is on the order of \(10^{100}\) years.

  2. The entire mass of the visible Universe is between \(10^{50}\) and \(10^{60}\) in size.

  3. How many different ways can you rearrange a deck of cards. That's \(50!\) which is about \(10^{67}\).

  4. The earth weighs about \(10^{28}\) grams. If you imagine a diamond that weighs as much as earth, it would contain about \(10^{50}\) carbon atoms. If you had a billion of those diamonds you would only have about \(10^{60}\) atoms.

So as you can see Googol is a very big number, but everything is relative. If you compared Googol to infinity it is very small. In fact it might as well be zero compared to infinity. I'll save infinity for another article.