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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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Last Updated 07/08/04 by JWB