Sci5
Name: _____________________________
Mr. Art
Date: ________________
Period: ______________
Multiplying & Dividing
Scientific Notation
-------------------------------------------------------------------------------------------------------------------------------Type #1: Multiplying in Scientific Notation Steps:
1) MULTIPLY the coefficients.
2) ADD the exponents of the two powers of 10 (Product Rule).
3) Check to see if the new coefficient is between 1 and 10.
a) If it is, keep it and skip to step 5.
b) If it isn't, go to step 4.
4) Change the new coefficient (that is not between 1 and 10) to a number that is between 1 and 10 by
moving the decimal point either to the right or left.
5) Right your answer in a  10n form.
a) If your new coefficient was already between 1 and 10, you are done.
b) If your new coefficient was not between 1 and 10, you are going to need to either add or subtract to
your new exponent. If , in step 4, you made your new coefficient smaller, you are going to make
your new exponent larger. If, in step 4, you made your new coefficient larger, you are going to
make your new exponent smaller.
-------------------------------------------------------------------------------------------------------------------------------Type #2: Dividing in Scientific Notation Steps:
1) DIVIDE the coefficients.
2) SUBTRACT the exponents of the two powers of 10 (Product Rule).
3) Check to see if the new coefficient is between 1 and 10.
a) If it is, keep it and skip to step 5.
b) If it isn't, go to step 4.
4) Change the new coefficient (that is not between 1 and 10) to a number that is between 1 and 10 by
moving the decimal point either to the right or left.
5) Right your answer in a  10n form.
a) If your new coefficient was already between 1 and 10, you are done.
b) If your new coefficient was not between 1 and 10, you are going to need to either add or subtract to
your new exponent. If , in step 4, you made your new coefficient smaller, you are going to make
your new exponent larger. If, in step 4, you made your new coefficient larger, you are going to
make your new exponent smaller.
Practice Examples
Directions: Perform the indicated operation (multiply or divide) to the two numbers in scientific notation.
1) Find the product of 2.6  10 7 and 6.3  10 4 .
3)
(4.4  10 6 )(3.9  10 4 )
5) Find the product of 2.8  10 8 and 1.9  10 4 .
7)
(1.3  10 9 )( 4.7  10 5 )
2) Find the quotient of 1.23  1011 and 2.4  10 4 .
4)
(5.76  10 9 )  (3.2  10 3 )
6)
3.72  10 8
1.2  10 5
8) Find the quotient of 6.4  10 4 and 910 .
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