Multiplying and Dividing Numbers in Scientific
Notation
Rule for Multiplication
When you multiply numbers with scientific notation,
multiply the coefficients together and add the
exponents. The base will remain 10.
(
) (
Example: Mulitiple 7.1 ! 105 ! 6.9 ! 10 4
)
7.1 ! 6.9 ! 105 ! 10 4
Using the commutative property
to change the order of the
factors you now have the
coefficients together on one side
and powers together on the right.
7.1 ! 6.9 ! 105 + 4
add the exponents using exponent
laws
48.99 ! 10 9
4.899 ! 101 ! 10 9
4.899 ! 1010
Multiply the coefficients
Change to proper scientific
notation form.
Correct Answer!!!
Rule for Division
When dividing with scientific notation, divide the
coefficients and subtract the exponents. The base
will remain 10.
Example: Divide
4.5 ! 10 9 by 5.79 ! 10 7
4.5 ! 10 9
5.79 ! 10
4.5
5.79
4.5
5.79
!
Rewrite the problem into
this form
7
10 9
10
7
! 10 9 " 7
Divide the coefiencents and
subtract the exponents .
Correct order for imputing
values into a calculator:
Press clear, enter 4.5,
press the division symbol ,
enter 5.79 and press equal.
0.78 ! 102
Not in proper form Change
to proper scientific notation
form.
7.8 ! 10
We subtract one from the
exponent because we moved
the decimal one place to
the right.