Date post: | 13-Dec-2015 |
Category: |
Documents |
Upload: | darleen-wood |
View: | 220 times |
Download: | 7 times |
Copyright © 2012, 2009, 2005, 2002 Pearson Education, Inc.
Section 5.2
Negative Exponents and
Scientific Notation
2Copyright © 2012, 2009, 2005, 2002 Pearson Education, Inc.
Negative Exponents
Definition of a Negative Exponent
where x 01nn
xx
3Copyright © 2012, 2009, 2005, 2002 Pearson Education, Inc.
Write with positive exponents.
a.4h
41h
b. 532a
5 153
1 1322
aa
Example
4Copyright © 2012, 2009, 2005, 2002 Pearson Education, Inc.
Negative Exponents
Laws of Exponents Where x, y, ≠ 0
The Product Rule
The Quotient Rule
Power Rules
a b a bx x x
aa b
b
xx
x Use if a > b. 1a
b b a
x
x x Use if a < b.
, , a a
ba a a a aba
x xxy x y x x
y y
5Copyright © 2012, 2009, 2005, 2002 Pearson Education, Inc.
Negative Exponents
Properties of Negative Exponents Where x, y, ≠ 0
1 nn
xx
m n
n m
x y
y x
6Copyright © 2012, 2009, 2005, 2002 Pearson Education, Inc.
Example
Simplify. Write the expression with no negative exponents.
a.3 5
2
x y
x y
3 2 5
5 6 x x xyy y
b. 34 22ab c 3 3 ( 4)( 3) (2)( 3)2 a b c
3 3 12 62 a b c12
3 3 62 b
a c
7Copyright © 2012, 2009, 2005, 2002 Pearson Education, Inc.
Scientific Notation
Scientific Notation A positive number is written in scientific notation if it is in the form a × 10n, where 1 a 10 and n is an integer.
8Copyright © 2012, 2009, 2005, 2002 Pearson Education, Inc.
Scientific Notation
8200 = 8.2 1000 = 8.2 103
34,200,000 = 3.42 10000000 = 3.42 107
Greater than 1 and less than 10
Power of 10
Scientific notation
9Copyright © 2012, 2009, 2005, 2002 Pearson Education, Inc.
Write 67,300 in scientific notation.
67,300. = 6.73 10n
The decimal point was moved 4 places to the left, so we use a power of 4.
67,300 = 6.73 104
A number that is larger than 10 and written in scientific notation will always have a positive exponent as the power of 10.
Example
10Copyright © 2012, 2009, 2005, 2002 Pearson Education, Inc.
Write 0.048 in scientific notation.
0.048 = 4.8 10n
The decimal point was moved 2 places to the right, so we use a power of –2.
0.048 = 4.8 10–2
A number that is smaller than 1 and written in scientific notation will always have a negative exponent as the power of 10.
Example
11Copyright © 2012, 2009, 2005, 2002 Pearson Education, Inc.
Write 9.1 104 in decimal notation.
9.1 104 = 9.1000 104= 91,000
Write 6.72 10–3 in decimal notation.
6.72 10–3= 6.72 10–3= 0.00672
Example
Move the decimal point 4 places to the right.
Move the decimal point 3 places to the left.
12Copyright © 2012, 2009, 2005, 2002 Pearson Education, Inc.
Example
Use scientific notation and the laws of exponents to find the following. Leave your answer in scientific notation.
32,000,000 1,500,000,000,000
7 123.2 10 1.5 10
7 123.2 1.5 10 10
194.8 10
Write each number in scientific notation.
Rearrange the order.
Multiply.
13Copyright © 2012, 2009, 2005, 2002 Pearson Education, Inc.
Example
Use scientific notation and the laws of exponents to find the following. Leave your answer in scientific notation.
0.00063
0.021
4
2
6.3 10
2.1 10
4
2
6.3 10
2.1 10
2
4
6.3 10
2.1 10
23.0 10
Write each number in scientific notation.
Rearrange the order.
Rewrite with positive exponents.