8.4 Scientific Notation
Scientific notation is used to write very large and very small numbers in powers of 10.
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
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
Scientific Notation to decimal form:
2.83 105
1.5 10-7
283,000
0.00000015
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!
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
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