Want to get a feeling for a Googol?
by Bob Frybarger
(This page uses the latest estimate of the Universe's age, currently 14 Billion Years!)
(Last Edit on April 26, 2002)

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, 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 8.852120611 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,
8.852120611 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,  3.910923629 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 pi r3

Let's cube the radius:  3.910923629 cubed is equal to  5.981883988, so multiply this number by 4,
and divide by 3 to get the result:  7.975845288 . And finally multiply that result by pi (3.1415927)
to get the number:  2.505685789

Now, 2.505685789 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 2.505685789, you will come to realize that you need
about 39 billion, 909 million, 940 thousand universes to be able to contain our googol of salt grains.