- What do you mean, orders of magnitude?

What would you say if someone asked you how big the universe is? Information from my astrophysics course has the experts saying 10^{60} centimeters. Can you even fathom a number that big? Most likely not.

Orders of magnitude can be spoken in terms of things besides distance. In mathematics, infinite magnitudes exist. Have you ever heard of a google? A google is 10^{100}. That is mighty big. Mathematicians also have coined the phrase googleplex, which is 10^{google}...that is 10^{10100}.

The previous discussion still does not clue us in to what orders of magnitude mean. The concept derives from scientific notation of numbers in which each order of magnitude is 10 times the previous one. For instance, 10 is one order of magnitude larger than 1. 100 is one order of magnitude larger than 10, but *two* orders of magnitude larger than 1.

Check this out!! This is a beautiful example of what we mean by orders of magnitude.

The bottom line is orders of magnitude allow us as scientists to have warm fuzzies in regards to how everything compares to everything else. Like the link...each frame is an order of magnitude closer to Earth starting from 10 million miles outside the Milky Way galaxy to the subatomic level until you are checking out a proton. How cool is that!?!

Generally we speak in terms of base 10 because we count in base 10. However, did you know computer scientists count in base 2 or base 8 or base 16. The space shuttle flight software is addressed and data is sent to the Mission Control Center in base 16.

10^{2} |
10^{1} |
10^{0} |

1 | 0 | 0 |

In base 16, the digits for the number 100 are as follows:

16^{2} |
16^{1} |
16^{0} |

1 | 0 | 0 |

In base 2, the digits for the number 100 are as follows:

2^{2} |
2^{1} |
2^{0} |

1 | 0 | 0 |

What do these numbers mean? It is 2 orders of magnitude larger than 1. In base 2 and in base 16, the same thing applies. How do these compare? Let's put the numbers in the same base as a means of seeing the difference between the numbers. We all know what 100 means in base 10. $100, 100%, 100 cookies (yum!). 100 in base 16 is 256 in base 10. 100 in base 2 is only 4 in base 10!

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These pages were made through TeacherTECH, the teacher professional development component of GirlTECH, which is sponsored by the Center for Excellence and Equity in Education (CEEE) with support from the National Science Foundation through EOT-PACI.

Copyright © June 2001 by Deanna Chipman.