1. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley P.1 Real Numbers

2. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide P- 2 Quick Review

3. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide P- 3 Quick Review Solutions

4. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide P- 4 What you’ll learn about Representing Real Numbers Order and Interval Notation Basic Properties of Algebra Integer Exponents Scientific Notation … and why These topics are fundamental in the study of mathematics and science.

5. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide P- 5 Real Numbers A real number is any number that can be written as a decimal. Subsets of the real numbers include: The natural (or counting) numbers: {1,2,3…} The whole numbers: {0,1,2,…} The integers: {…,-3,-2,-1,0,1,2,3,…}

6. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide P- 6 Rational Numbers Rational numbers can be represented as a ratio a/b where a and b are integers and b≠0. The decimal form of a rational number either terminates or is indefinitely repeating.

7. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide P- 7 The Real Number Line

8. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide P- 8 Order of Real Numbers Let a and b be any two real numbers. SymbolDefinitionRead a>ba – b is positivea is greater than b a<ba – b is negativea is less than b a≥ba – b is positive or zeroa is greater than or equal to b a≤ba – b is negative or zeroa is less than or equal to b The symbols >, <, ≥, and ≤ are inequality symbols.

9. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide P- 9 Trichotomy Property Let a and b be any two real numbers. Exactly one of the following is true: a b.

10. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide P- 10 Example Interpreting Inequalities Describe the graph of x > 2.

11. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide P- 11 Example Interpreting Inequalities Describe the graph of x > 2. The inequality describes all real numbers greater than 2.

12. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide P- 12 Bounded Intervals of Real Numbers Let a and b be real numbers with a < b. Interval NotationInequality Notation [a,b]a ≤ x ≤ b (a,b)a < x < b [a,b)a ≤ x < b (a,b]a < x ≤ b The numbers a and b are the endpoints of each interval.

13. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide P- 13 Unbounded Intervals of Real Numbers Let a and b be real numbers. Interval NotationInequality Notation [a,∞)x ≥ a (a, ∞)x > a (-∞,b]x ≤ b (-∞,b)x < b Each of these intervals has exactly one endpoint, namely a or b.

14. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide P- 14 Properties of Algebra

15. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide P- 15 Properties of Algebra

16. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide P- 16 Properties of the Additive Inverse

17. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide P- 17 Exponential Notation

18. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide P- 18 Properties of Exponents

19. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide P- 19 Example Simplifying Expressions Involving Powers

20. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide P- 20 Example Simplifying Expressions Involving Powers

21. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide P- 21 Example Converting to Scientific Notation Convert 0.0000345 to scientific notation.

22. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide P- 22 Example Converting to Scientific Notation Convert 0.0000345 to scientific notation.

23. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide P- 23 Example Converting from Scientific Notation Convert 1.23 × 10 5 from scientific notation.

24. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide P- 24 Example Converting from Scientific Notation Convert 1.23 × 10 5 from scientific notation. 123,000