Scientific notation is a compact way of writing very large or very small numbers. A number written in scientific notation follows the form $$\begin{array}{c}a\times 10^b\end{array}$$ where $1\le a<10$ and $b$ is an integer. For example, the number $4$ million can be rewritten as the product of $4$ and a multiple of $10.$ Then, the multiple of $10$ is rewritten as a base $10$ power. $$\begin{array}{c}4000000=4\times 1000000=4\times 10^6\end{array}$$ Scientific notation can also be applied to very small decimal numbers, where there are many zeros before the significant figures, such as $0.000342.$ $$\begin{array}{c}0.000342=3.42÷10000=3.42\times 10^{\text{-}4}\end{array}$$ In such cases, numbers are rewritten as a division by a multiple of $10.$ Division by a multiple of $10$ is equivalent to multiplication by a base $10$ power with negative exponent. Below are a few more examples of numbers written in scientific notation.

Decimal Form	Write as a product or division	Scientific Notation
$4505$	$4.505\times 1000$	$4.505\times 10^3$
$8320000$	$8.32\times 1000000$	$8.32\times 10^6$
$0.0005$	$5÷10000$	$5\times 10^{\text{-}4}$
$0.0521$	$5.21÷100$	$5.21\times 10^{\text{-}2}$

An intuitive way to rewrite a number greater than $10$ in scientific notation is done by counting the number of places the decimal needs to move so the number is greater than or equal to $1$ and less than $10.$ The number of places the decimal moved from right to left indicates the exponent to be used for the base $10$ power.

Similarly, for numbers less than $1,$ such as $0.000022,$ the decimal will move from left to right. In this case, the number of places moved indicates the negative exponent to be used for the base $10$ power.