11) A Fable

Are there numbers even bigger than a trillion? Yes there are! But why would we need such big numbers?

There are many different occupations in which people work with large (and small) numbers: bankers, finance companies, real estate brokers, and anyone else who deals with money.

Let me tell you an interesting fable.

The story goes that the ruler or India was so pleased with one of his palace wise men, who had invented the game of chess, that he offered this wise man a reward of his own choosing.

The wise man, who was also a wise mathematician, told his Master that he would like just one grain of rice on the first square of the chess board, double that number of grains of rice on the second square, and so on: double the number of grains of rice on each of the next 62 squares on the chess board.

 

This seemed to the ruler to be a modest request, so he called for his servants to bring the rice. How surprised he was to find that the rice quickly covered the chess board, then filled the palace! Let's stop here, and see just how many grains of rice this is.

The number of grains of rice on the last square can be written as "2 to the 63th power", which looks like this:

263

This means:

2 times 2 times 2 times 2 times 2 times 2 times 2 times 2 times 2 times 2 times 2 times 2 times 2 times 2 times 2 times 2 times 2 times 2 times 2 times 2 times 2 times 2 times 2 times 2 times 2 times 2 times 2 times 2 times 2 times 2 times 2 times 2 times 2 times 2 times 2 times 2 times 2 times 2 times 2 times 2 times 2 times 2 times 2 times 2 times 2 times 2 times 2 times 2 times 2 times 2 times 2 times 2 times 2 times 2 times 2 times 2 times 2 times 2 times 2 times 2 times 2 times 2 times 2

. . . or "2 times itself 63 times".

Which can be written as approximately: 18,446,744,070,000,000,000 (I can't write this more accurately as I have only 10 spaces on my TI-34 calculator!)

A grain of rice is approximately .2 inches long. Converting .2 inches to feet (divide by 12 inches to a foot) and then dividing that number by 5,280 feet in one mile, we get the length of the grains of rice, placed end-to-end, to be approximately 60,000,000,000,000 miles. How far is that? Alpha Centauri, the nearest star, is located 25,000,000,000,000 miles from Earth. Placed end to end, these grains of rice would reach farther than from the Earth, across space to the nearest star, Alpha Centauri, and back to Earth again!

Go to Topic 12: Scientific Notation