Download 9.4 Scientific Notation

9.4 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
9.3 ∙ 107
.00000625
6.25 ∙ 10-6
Examples:
2450 = 2.45 x 103
1.78 = 1.78 x 100
0.000722 = 7.22 x 10-4
Scientific Notation to Decimal Form:
2.83 ∙ 105
283,000
1.5 ∙ 10-7
0.00000015
Examples:
1.345 x 102 = 134.5
3.67 x 104 = 36,700
7.8 x 10-1= 0.78
4.103 x 10-5 = 0.00004103
Multiplying Scientific Notation:
(3.2 x 106) (4.2 x 104)
Combine like terms
3.2 ∙ 4.2 ∙ 106 ∙ 104
Multiply numbers
and add exponents
13.44 x 1010
1.344 x 1011
Pull out another positive power
of 10, so 1010 + 101 = 1011!
Multiplying Scientific Notation:
(1.4 x 104) (7.6 x 103)
Combine like terms
1.3 ∙ 7.6 ∙ 104 ∙ 103
Multiply numbers
and add exponents
10.64 x 107
1.064 x 108
Pull out another positive power
of 10, so 107 + 101 = 108!
Dividing with Scientific Notation:
4.5 x 10-7
9.0 x 10-4
4.5 x 10-7
9.0 x 10-4
Rewrite as a product of fractions
0.5 ∙ 10-7-(-4) Divide and subtract exponents
0.5 ∙ 10-3
Simplify
5 x 10-4
0.0005 Scientific notation
Dividing with Scientific Notation:
1.2 x 10-1
4.8 x 10-4
1.2 x 10-1
4.8 x 10-4
Rewrite as a product of fractions
0.25 ∙ 10-1-(-4) Divide and subtract exponents
0.25 ∙ 103
Simplify
2.5 x 102
250 Scientific notation
Homework
page 422 #6-26 even, 33-35
Study for 9.1-9.4 quiz Tuesday