Multiplying and Dividing in Scientific Notation

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Multiplying and Dividing in Scientific Notation
Multiplying and dividing in scientific notation is a little different then adding and
subtracting
 The biggest difference is that if the exponents are not the same in multiplication
and division problems, we can still compute with them.
o For example, these are all problems we can solve:
1. 7.01  10 5  5.63  10 5
2. 4.8  10 2  2.4  10 6
3. 7.792  10 6  3.578  10 6
4. 6.2  10 3   3.17  10 7
Here is an example of how we multiply in scientific notation:
 Multiply: 6.2  10 3   3.17  10 7
o To multiply this, we do 2 steps:
1. Multiply the decimals
 6.2   3.17  19.654
2. Subtract our exponents
 -3-7=-10
o So our answer becomes  19.654  10 10
 That answer is not in scientific notation, se we need to move our
decimal over to the left once, and add 1 to our exponent
 So our answer will become:
o  19.654  10 10  1.9654  10 9
Here is an example of how to divide in scientific notation:
 Divide: 3.9  108  6.5  10 4
o To divide this, we de 2 steps:
1. Divide the decimals
 3.9  6.5  0.6
2. Subtract your exponents
 8-(-4)=12
o So our answer becomes: 0.6  1012 .
 That answer is not in scientific notation, so we need to move our
decimal over to the right once, and subtract 1 from our exponent.
 So our answer will become:
o 0.6  1012  6.0  1011
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