Scientific Notation

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 10^{9}. Thus
and a number like 2345 becomes
For very small numbers we use negative powers of ten. Recall that
so, for example a thousandth becomes 10^{3} because
Calculator NoteScientific calculators will work in scientific notation, but most of them do not display the " ´ 10" part. To enter a number such as 2.3 ´ 10^{5}, you would

Last Updated 07/08/04 by JWB 