Scientific Notation
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Physics deals with numbers that are very small and numbers that are very large. For example, we talk about distances on the atomic scale of less than a billionth of an inch, and when we are talking about stars and galaxies the distances are trillions of miles. Scientific notation is a method that lets us write these very large and very small numbers in a compact form. This is done by writing the number as a number between one and ten, multiplied by a power of ten. For example, the number 2 billion is a 2 followed by nine zeros, or 2,000,000,000. In scientific notation we would see it as 2 times a billion, where a billion can be expressed as 109. Thus

2,000,000,000 = 2 109

and a number like 2345 becomes

2.345 103.

For very small numbers we use negative powers of ten. Recall that

,

so, for example a thousandth becomes 10-3 because

.

Calculator Note

Scientific calculators will work in scientific notation, but most of them do not display the " 10" part. To enter a number such as 2.3 105, you would

  1. enter the 2.3
  2. press a button that says EE or sometimes EXP
  3. then enter the exponent, in this case 5.
  4. if the exponent is negative, on most calculators you would press the negation button (the plus or minus button) after you enter the exponent. On some, though, you press it first, so you might have to experiment (or read the instructions).
 

 

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Copyright 2000-2001
  James W. Brennan
Selland College of Applied Technology
Boise State University

Last Updated 07/08/04 by JWB