An application of Powers is the scientific notation of numbers. The underlying basic fact is that a power of 10 whose exponent is a natural number can be easily evaluated: the exponent gives the number of zeros. For example:

Negative exponents may be used to indicate numbers smaller than , e.g.,

**Scientific Notation** is used to indicate numbers that are very large
or very small.
We write a number as a factor whose absolute
values is between and , and a power of . That power
is indicated either by an actual power with an exponent, or the letter
followed by just the exponent.

Here are some examples:

- First some numbers:
A light year is the distance covered at the speed of light in one year. It equals approximately

The radius of the visible universe is (very) roughly 10 billion light years or miles. It contains (again very roughly) atoms.

It is worthwhile to know the words that describe the powers of 10, as
in this table:
- The federal deficit is about , or $5 trillion. It will be a long time before we run out of words that describe it.
- A googol is a followed by a 100 zeros, or
. A googolplex is a followed by a googol zeros, or
. In scientific notation a googolplex
is
- The decimal system uses prefixes to indicate factors that are powers
of 10, as follows:
So for example, one

*km*is 1,000 meters, and a*cm*is one hundredth of a meter. (A*meter*is 3.28 feet.) However, computers use as the base of its number system. So in the computer industry

*kilo*means multiply with ,*mega*means multiply with , and*giga*means multiply with You can look at this either as getting more in your computer than you asked for, or the computer industry hopelessly and ruthlessly confusing Math 1010 students.