Chapter 4

Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter 4-1

Exponents and Polynomials

2 Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter 4-2

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

Chapter Sections

3 Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter 4-3

Scientific Notation

4 Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter 4-4

Scientific NotationA 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

5 Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter 4-5

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 1.1543

2. 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

6 Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter 4-6

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

7 Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter 4-7

Converting from Scientific Notation

1. Observe the exponent of the power of 10.3.8 x 104 Exponent is +4

2. 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 places

3.8 x 104 = 38000

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.

8 Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter 4-8

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 = 0.000384 places

9 Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter 4-9

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

10 Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter 4-10

Recognize Numbers in Scientific Notation with a Coefficient of 1

11 Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter 4-11

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

12 Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter 4-12

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