The Exponents - What are Exponents? answers questions


How many times would you have to fold a piece
of paper to get to the Moon?

Using exponents is a short way of saying "multiply the number by itself." The little number up above tells you how many times to multiply the number by itself. So 102 means 10 x 10, or 100. We call this 10 squared because if you wanted to find the area of a square whose sides were 10 inches long, you'd have to multiply 10 x 10 to get 100 square inches.

In the same way, 103 means 10 x 10 x 10, or 1000. (Notice that each time you have an exponent of 10, the little number up above tells you how many zeros there will be in the answer). We call this 10 cubed, because if you wanted to find the volume of a cube whose sides were 10 inches long, you'd have to multiply 10 x 10 x 10 to get 1000 cubic inches.

Exponents also work with other numbers besides 10. If your square was only 4 inches on a side, you'd find the area by calculating 42, or 4 x 4= 16 square inches. To find the area of a cube 4 inches on a side, you'd calculate 43, or 4 x 4 x 4 = 64 cubic inches.

Now you can understand two very big numbers that people sometimes talk about. One is a googol. A googol is 10100, which means 10 x 10 a hundred times (It was actually a nine-year-old boy who came up with the name). A googol is a large number - 1 with a hundred zeroes after it. A googol is bigger than the number of sub-atomic particles in the known universe. On the other hand, a googol is smaller than the number of possible different games of chess (about 10120).

The second very big number is called a googolplex (also named by the same kid, Milton Sirotta). A googolplex is 10googol, or 1 with a googol zeroes after it. We can't even write that many zeroes down, even if all the matter in the Universe was turned into paper, and if you wrote two numbers a second, it would take you longer than the age of the universe to write it down.

Even though a googolplex is not really a useful number, it can help you to remember that when you use exponents, you can get to big numbers very quickly. Two is a small number, but 22 is 4, and 23 is 8, and 24 is 16, and 25 is 32, and 26 is 64, and 27 is 128, and so on. It doubles every time you increase the exponent. The higher you go with the exponents, the quicker your number gets bigger.

When you draw exponential numbers on a number plane, you end up with a parabola.

An Islamic story using exponents
More about Numbers

Bibliography and further reading about numbers:

Wheat on the Chessboard
More about Math home

Professor Carr

Karen Eva Carr, PhD.
Assoc. Professor Emerita, History
Portland State University

Professor Carr holds a B.A. with high honors from Cornell University in classics and archaeology, and her M.A. and PhD. from the University of Michigan in Classical Art and Archaeology. She has excavated in Scotland, Cyprus, Greece, Israel, and Tunisia, and she has been teaching history to university students for a very long time.

Professor Carr's PSU page

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