1. Ch1.8_NegativeExponentsAndScientificNotation.notebook August 31, 2011
Warm­Up
Simplify
a 5
(b)
2 3 2
(a bc )
Chapter 1.8
Negative Exponents
and Scientific Notation
1

2. Ch1.8_NegativeExponentsAndScientificNotation.notebook August 31, 2011
Recap
22 = (2)(2)
24 = (2)(2)(2)(2)
Recap
3
2 = (2)(2)(2)
1
2 (2)
2
(2)(2) = 2
3
2 = 3­1
1 2
2
2

3. Ch1.8_NegativeExponentsAndScientificNotation.notebook August 31, 2011
Negative Exponents
3
2 = 3 ­ 5
5 2
2
­2
2
3
2 = (2)(2)(2)
5
2 (2)(2)(2)(2)(2)
New Idea a­n = 1
an
­1
3 =
­3
2 =
4­2 =
­22
x =
3

4. Ch1.8_NegativeExponentsAndScientificNotation.notebook August 31, 2011
New Idea n 1
a = ­n
a
1
­2 =
3
1
­2 =
2
1
­16 =
a
General Rule
If the negative exponent is in the numerator,
it moves to the denominator to be positive
If the negative exponent is in the denominator,
it moves to the numerator to be positive
4

5. Ch1.8_NegativeExponentsAndScientificNotation.notebook August 31, 2011
Rewrite with only POSITIVE exponents
­2
a
­3
x
Rewrite with only POSITIVE exponents
­1 2 4
a bc
5 ­4 ­2
xy z
5

6. Ch1.8_NegativeExponentsAndScientificNotation.notebook August 31, 2011
Rewrite with only POSITIVE exponents
6 12
r ÷ r
­7 3
(m )
Evaluate if x=2
2 ­5
x x
6

7. Ch1.8_NegativeExponentsAndScientificNotation.notebook August 31, 2011
Scientific Notation
A quicker way to write very large or
small numbers using powers of 10
Scientific Notation
345,000,000.
3.45 x 100,000,000.
8
3.45 x 10
7

8. Ch1.8_NegativeExponentsAndScientificNotation.notebook August 31, 2011
Scientific Notation
Step 1: Locate the non­zero digits
98,400,000.
Step 2: Move the decimal so that it is
between the first and second non­zero digits
9.8400000
Step 3: Count the number of spaces moved
(this is the power of 10)
9.8400000
[ 7 spaces ]
9.84 x 107
Rules
If the number is very large (greater than 10),
the exponent is positive
456,000.
4.56 x 105
If the number is very small (less than 1),
the exponent is negative
0.00824
­3
8.24 x 10
8

9. Ch1.8_NegativeExponentsAndScientificNotation.notebook August 31, 2011
Write the following numbers
in scientific notation
370,000
.00123
Write the following numbers
in standard form
3.859 x 104
­3
8.726 x 10
9

10. Ch1.8_NegativeExponentsAndScientificNotation.notebook August 31, 2011
Page 40
8­44 evens
10