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8.4 Scientific Notation
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Scientific notation is used to write very large and very small numbers in powers of 10.
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Decimal form Power of 10 Name
1,000,000,000 109 one billion
1,000,000 106 one million
1,000 103 one thousand
100 102 one hundred
10 101 ten
1 100 one
.1 10-1 one tenth
.01 10-2 one hundredth
.001 10-3 one thousandth
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Form: c 10n where c is a number > 1 and <10
Change decimals to scientific notation:
93,000,000
.00000625
9.3 107
6.25 10-6
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Scientific Notation to decimal form:
2.83 105
1.5 10-7
283,000
0.00000015
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Multiplying Scientific notation:
(3.2 106) ( 4.2 104)
3.2 4.2 106 104
13.44 1010
1.344 1011
Combine like terms
Multiply numbers and add exponents
Pull out another positive power of 10, so 1010 + 101 = 1011!
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Dividing with scientific notation:
4.5 10-7
9.0 10-4
.5 10-7-(-4)
.5 10-3
5 10-4 .0005
Divide numbers
Subtract exponents
Simplify.
or