Want to get a feeling for a Googol?

by Bob Frybarger

(This page uses the latest (2004) estimate of the Universe's age, currently 14 Billion Years!)

Remember the Carl Sagan PBS series "Cosmos"?  In one episode, Carl spoke of a large number he called a googol. 
It turns out that this "googol" is an accepted number by the mathematics community, and is defined as 1 followed by 100 zeros!
A large number indeed.  Mr. Sagan wrote on a piece of paper, a "1" and followed it with one hundred zeros, then folded the
paper, looked at the camera and told the audience that a googol of these pieces of paper would not fit into the known universe.

I thought about that idea for a considerable time, and then dismissed it as unimaginable. We humans have a hard
time imagining a million of anything, let alone a billion or a trillion! After trying for a long time to imagine how large a number a
googol really is, I came up with a thought experiment. My assumption is that everyone everywhere could visualize a grain of
table salt. Therefore, let's line up some salt, and do a little calculating!

It turns out that I counted 75 grains of table salt in a linear inch, and so now we have a start. If we multiply 75 times
12, we find there are 900 salt grains in a linear foot. Multiply that 900 times 5,280 and we find 4,752,000 grains in a linear mile.
Multiply 4,752,000 times 186,282 (the speed of light) and there are 8.852E+11 grains of salt in a line, one light-second long.

If we keep up the multiplication to find how many grains of salt there are in a line to the edge of the known universe
(approximately 14 billion light years), we need to multiply our result so far, 8.852E+11 by 60 (seconds in a minute), by 60
again (minutes in an hour), by 24 (hours in a day), by 365.24 (days in a year), and by 14 billion (age of the universe)...
This number is huge, 3.910E+29 but it is only the number of grains in a single line to the edge of the universe.

By the way, it is not even close to a googol......

Now we need to find the volume of the universe, and how many grains of salt it could hold. The formula for volume
is:  Vol = 4/3 ╥ r3.†† Let's cube the radius:  3.910E+29 cubed is equal to 5.981E+88, so multiply this number by 4, and divide by
3 to get the result: 7.975E+88 .And finally multiply that result by ╥ (3.1415927)
to get the number:  2.505E+89

Now, 2.505E+89 is a very, very large number, but are we at a googol yet?

This huge number represents the grains of table salt that you could get into our universe, and it is not even remotely close to my
proposed googol of salt grains!!!

If you will FINALLY divide a googol by 2.505E+89, you will come to realize that you need about 39 billion, 900
million universes to be able to contain our googol of salt grains.

Now I ask, is that an amazing visualization???  My head hurts

© 1999


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(Many thanks to Russ Wolfe for his help cleaning up my notation errors on this page)