Scientific Notation

Making large and small numbers more manageable.

Scientific notation is a system for representing a number as a number between 1 and 10 multiplied by a power 10.

Scientific nation is most useful for presenting very large or very small numbers in a form that is easier to use.

For example: The sets of numbers below are equivalent. However, the numbers of the right can be read much more easily.

253,000,000,000,000,000,000 = 2.53 x 1020

0.0000000000000000000253 = 2.53 x 10-20

In scientific notation, numbers are expressed as a number between 1 and 10 multiplied by 10 raised to an exponent.

120.3 = 1.203 x 100

100 is the same as 102

In scientific notation, numbers are expressed as a number between 1 and 10 multiplied by 10 raised to an exponent.

120.3 = 1.203 x 102

100 is the same as 102

In scientific notation, numbers are expressed as a number between 1 and 10 multiplied by 10 raised to an exponent.

1203 = 1.203 x 1000

1000 is the same as 103

In scientific notation, numbers are expressed as a number between 1 and 10 multiplied by 10 raised to an exponent.

1203 = 1.203 x 103

1000 is the same as 103

In scientific notation, numbers are expressed as a number between 1 and 10 multiplied by 10 raised to an exponent.

0.1203 = 1.203 x 10-1

1/10 is the same as 10-1

In scientific notation, numbers are expressed as a number between 1 and 10 multiplied by 10 raised to an exponent.

An easy way to determine the exponent of ten is to count the decimal positions you move.

0.000001203 = 1.203 x 10-6

The decimal has moved backwards: 6 positions

In scientific notation, numbers are expressed as a number between 1 and 10 multiplied by 10 raised to an exponent.

An easy way to determine the exponent of ten is to count the decimal positions you move.

1203000000 = 1.203 x 109

The decimal has moved forwards: 9 positions

Practice Questions:

74,390,000 = __________ x 10_

0.000009998 = _________ x 10_

-0.0000623 = __________ x 10_

5.466 x 106 = __________2.3 x 10-4 = ___________

Scientific notation makes it easier to express very large or very small numbers in more manageable terms. It is used widely in the scientific community when referencing everything from numbers of bacterial to concentrations of solution.

Concept Question

How would you express a number such as 1.5 or 0.2 in scientific notation?