Scientific notation is a compact way of writing very large or very small numbers. A number written in scientific notation is expressed as a product of two numbers. In this form, the first factor is greater than or equal to $1$ and less than $10.$ In other words, it needs to be in the interval $[1,10).$ The second factor is a power of $10$ where $b$ 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. Very small decimal numbers can also be written in scientific notation. Consider a number where there are many zeros before the significant figures. Take as $0.000342$ as an example. In such cases, numbers are expressed as a division by a multiple of $10.$ Division by a multiple of $10$ is equivalent to multiplication by a base $10$ power with a negative exponent. Consider a few more examples of numbers written in scientific notation.

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

Intuitive Method: Rewriting a Number in Scientific Notation

An intuitive method to rewrite a number into scientific notation is to count the number of places the decimal needs to move. Consider a number greater than $10.$ The decimal would move from right to left to make the number less than $10$ but still greater than $1.$ The number of places the decimal moved indicates the positive 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 to make the number greater than or equal to $1$ and less than $10.$ In this case, the number of places moved indicates the negative exponent to be used for the base $10$ power. Scientific notation is not only a convenient way to express cumbersome numbers. It also eases the comparison of numerical order of magnitude. For example, it may be difficult to determine how much larger $237000000$ is compared to $4530000.$ However, it is easier to see that $2.37\times 10^8$ and $4.5\times 10^6$ differ by a factor of about $10^2=100.$