Scientific Notation

It is not unusual to encounter very small or very large numbers during a scientific investigation. But, these numbers are inconvenient to write and can be confusing when attempting to maintain accuracy. Therefore, scientists usually express numbers using scientific notation.

Scientific notation makes very large numbers or very small numbers easier to work with in calculations and data. It also provides a way to show the appropriate significant figures when there are several zeroes involved.

Scientific notation is based on the powers of ten and is written in the following form:

#.### x 10ⁿ  or #.### x 10^-n

Notice that in order to be in proper scientific notation there should only be one leading digit followed only by the significant digits.

Scientific Notation Rules

1. Move the decimal point to the right or the left in order obtain only one leading digit.
2. If the decimal is moved to the right, then subtract from the power of 10 the number of times you moved the decimal.
3. If the decimal is moved to the left, then add to the power of 10 the number of times you moved the decimal.

Example:  5,230 = 5.23 x 103 or .00523 = 5.23 x 10-3

Practice

PDF Handout