Scientific notation is a method of representing a number by using the decimal form of that number multiplied by a factor of 10.

Scientific notation 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 shown here are equivalent.
                      However, the numbers on the right can be read much
                      more easily.

                     253,000,000,000,000,000,000 = 2.53 × 1020

                      0.0000000000000000000253 =

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

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

00000

= 1.203 × 109

3

Instructions:
Express the following number using scientific notation.

Question 1:

74,390,000 =

× 10

Instructions:
Express the following number using scientific notation.

Question 2:

0.000009998 =

× 10

Instructions:
Express the following number using scientific notation.

Question 3:

× 10

Instructions:
Express the following numbers in their long forms.

Question 4:

5.466 × 106 =

Instructions:
Express the following numbers in their long forms.

Question 5:

2.3 × 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 bacteria to concentrations of solution.

You have to move the decimal point 7 places to the left so the exponent is 7.

74,390,000 = 7.439 × 107

0.000009998 = 9.998 × 10−6

-0.0000623 = -6.23 × 10−5

The exponent is 6 so you have to move the decimal point 6 positions to the right.

5.466 × 106 = 5466000

2.3 × 10−4 = 0.00023