Department of Mathematics --- College of Science --- University of Utah

Mathematics 1010 online

Scientific Notation

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:

\begin{displaymath}
\begin{array}{rcr}
10^0 &=& 1 \\
10^1 &=& 10 \\
10^3 &=& 1,000 \\
10^6 &=& 1,000,000 \\
\end{array} \end{displaymath}

Negative exponents may be used to indicate numbers smaller than $ 1 $, e.g.,

\begin{displaymath}
\begin{array}{rcccl}
10^{-1} &=& \displaystyle\frac{1}{10} &...
...\displaystyle\frac{1}{1,000,000} &=& 0.000001 \\
\end{array} \end{displaymath}

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 $ 1 $ and $ 10 $, and a power of $ 10 $. That power is indicated either by an actual power with an exponent, or the letter $ E $ followed by just the exponent.

Here are some examples: