Download Exponents and Polynomials Chapter 4

Chapter 4
Exponents
and
Polynomials
Copyright © 2015, 2011, 2007 Pearson Education, Inc.
Chapter 4-1
Chapter Sections
4.1 – Exponents
4.2 – Negative Exponents
4.3 – Scientific Notation
4.4 – Addition and Subtraction of Polynomials
4.5 – Multiplication of Polynomials
4.6 – Division of Polynomials
Copyright © 2015, 2011, 2007 Pearson Education, Inc.
Chapter 4-2
2
Scientific Notation
Copyright © 2015, 2011, 2007 Pearson Education, Inc.
Chapter 4-3
3
Scientific Notation
A number written in scientific notation is
written as a number greater than or equal to 1
and less than 10 (1 a  10) multiplied by
some power of 10. The exponent on the 10
must be an integer.
Example:
a.) 1.2 x 106
b.) 3.762 x 103
Copyright © 2015, 2011, 2007 Pearson Education, Inc.
Chapter 4-4
4
Writing in Scientific Notation
1.
Move the decimal point in the original number to the
right of the first nonzero digit. This will give a
number greater than or equal to 1 and less than 10.
11,543
2.
1.1543
Count the number of places you moved the decimal
point to obtain the number in step 1. If the original
number was 10 or greater, the count is positive. If the
original number was less then 1, the count is
considered negative.
1.1543
4 places
Copyright © 2015, 2011, 2007 Pearson Education, Inc.
Chapter 4-5
5
Writing in Scientific Notation
3.
Multiply the number obtained in step 1 by 10
raised to the count (power) found in step 2.
1.1543
104
4 places
11,543 = 1.1543 x 104
Example:
a.) 18,500 = 1.84 x 104
b.) 0.0000416 = 4.16 x 10-5
Copyright © 2015, 2011, 2007 Pearson Education, Inc.
Chapter 4-6
6
Converting from Scientific Notation
1.
Observe the exponent of the power of 10.
3.8 x 104
2.
Exponent is +4
a) If the exponent is positive, move the decimal point in
the number to the right the same number of places as the
exponent. (This will result in a number greater than or
equal to 10.)
4
3.8 x 10 = 38000
4 places
b) If the exponent is 0, do not move the decimal point.
Drop the factor 100 since it equals 1. This will result in a
number greater than or equal to 1 but less than 10.
Copyright © 2015, 2011, 2007 Pearson Education, Inc.
Chapter 4-7
7
Converting from Scientific Notation
c) If the exponent is negative, move the decimal point in
the number to the left the same number of places as the
exponent. (This will result in a number less than 1.)
3.8 x 10-4 = 0.00038
4 places
Copyright © 2015, 2011, 2007 Pearson Education, Inc.
Chapter 4-8
8
Calculations Using Scientific Notation
a.) 2.9 x 104 = 2.9 x 10,000= 29,000
b.) 6.28 x 10-3 = 0.00628
c.) 7.95 x 108 = 795,000,000
Copyright © 2015, 2011, 2007 Pearson Education, Inc.
Chapter 4-9
9
Recognize Numbers in Scientific Notation
with a Coefficient of 1
Copyright © 2015, 2011, 2007 Pearson Education, Inc.
Chapter 4-10
10
Recognize Numbers in Scientific Notation with
a Coefficient of 1
Example: Write the quantity without the given
metric prefix and then express the answer in
scientific notation.
The diameter of a human hair may be 100 micrometers.
100µm = 100 x 10-6 meters = 0.0001 meters =
1 x 10-4 meters
Copyright © 2015, 2011, 2007 Pearson Education, Inc.
Chapter 4-11
11
Do Calculations Using Scientific Notation
We can use the rules of exponents presented in Sections
4.1 and 4.2 when working with numbers written in
scientific notation.
Example: Multiply (4.2 x 106)(2.0 x 10-4). Write the
answer in decimal form.
(4.2 x 106)(2.0 x 10-4) = (4.2 x 2.0)(106 x 10-4)
= 8.4 x 106 + (-4)
= 8.4 x 102
= 840
Copyright © 2015, 2011, 2007 Pearson Education, Inc.
Chapter 4-12
12