2. CHAPTER 9 Introduction to Real Numbers and Algebraic Expressions Slide 2Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. 9.1Introduction to Algebra 9.2The Real Numbers 9.3Addition of Real Numbers 9.4Subtraction of Real Numbers 9.5Multiplication of Real Numbers 9.6Division of Real Numbers 9.7Properties of Real Numbers 9.8Simplifying Expressions; Order of Operations

3. OBJECTIVES 9.2 The Real Numbers Slide 3Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. aState the integer that corresponds to a real-world situation. bGraph rational numbers on the number line. cConvert from fraction notation for a rational number to decimal notation.

4. OBJECTIVES 9.2 The Real Numbers Slide 4Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. dDetermine which of two real numbers is greater and indicate which, using. Given an inequality like a > b write another inequality with the same meaning. Determine whether an inequality like –3 5 is true or false. eFind the absolute value of a real number.

5. 9.2 The Real Numbers a State the integer that corresponds to a real-world situation. Slide 5Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. A set is a collection of objects. For our purposes, we will most often be considering sets of numbers. One way to name a set uses what is called roster notation. For example, roster notation for the set containing the numbers 0, 2, and 5 is {0, 2, 5}. Sets that are part of other sets are called subsets.

6. 9.2 The Real Numbers NATURAL NUMBERS Slide 6Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. The set of natural numbers = {1, 2, 3,…}. These are the numbers used for counting.

7. 9.2 The Real Numbers WHOLE NUMBERS Slide 7Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. The set of whole numbers = {0, 1, 2, 3,…}. This is the set of natural numbers and 0.

8. 9.2 The Real Numbers a State the integer that corresponds to a real-world situation. Slide 8Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.

9. 9.2 The Real Numbers INTEGERS Slide 9Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.

10. 9.2 The Real Numbers a State the integer that corresponds to a real-world situation. Slide 10Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.

11. 9.2 The Real Numbers a State the integer that corresponds to a real-world situation. Slide 11Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. We call the integers to the left of zero negative integers. The natural numbers are also called positive integers. Zero is neither positive nor negative. We call –1 and 1 opposites of each other.

12. EXAMPLE 9.2 The Real Numbers a State the integer that corresponds to a real-world situation. 4Stock Price Change Slide 12Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. Tell which integers correspond to this situation: Hal owns a stock whose price decreased $16 per share over a recent period. He owns another stock whose price increased $2 per share over the same period. The integer –16 corresponds to the decrease in the value of the first stock. The integer 2 represents the increase in the value of the second stock.

13. 9.2 The Real Numbers RATIONAL NUMBERS Slide 13Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.

14. 9.2 The Real Numbers b Graph rational numbers on the number line. Slide 14Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. To graph a number means to find and mark its point on the number line.

15. EXAMPLE 9.2 The Real Numbers b Graph rational numbers on the number line. 6 Slide 15Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.

16. EXAMPLE 9.2 The Real Numbers b Graph rational numbers on the number line. 7 Slide 16Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.

17. EXAMPLE 9.2 The Real Numbers c Convert from fraction notation for a rational number to decimal notation. 8 Slide 17Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. We first find decimal notation

18. EXAMPLE 9.2 The Real Numbers c Convert from fraction notation for a rational number to decimal notation. 9 Slide 18Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. We can abbreviate repeating decimal notation by writing a bar over the repeating part—in this case, we write

19. 9.2 The Real Numbers Slide 19Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. Each rational number can be expressed in either terminating or repeating decimal notation.

20. 9.2 The Real Numbers Slide 20Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. Decimal notation for rational numbers either terminates or repeats. Decimal notation for irrational numbers neither terminates nor repeats.

21. 9.2 The Real Numbers d Determine which of two real numbers is greater and indicate which, using. Given an inequality like a > b write another inequality with the same meaning. Determine whether an inequality like –3 5 is true or false. Slide 21Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.

22. 9.2 The Real Numbers REAL NUMBERS Slide 22Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. The set of real numbers = The set of all numbers corresponding to points on the number line.

23. 9.2 The Real Numbers d Determine which of two real numbers is greater and indicate which, using. Given an inequality like a > b write another inequality with the same meaning. Determine whether an inequality like –3 5 is true or false. Slide 23Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.

24. 9.2 The Real Numbers d Determine which of two real numbers is greater and indicate which, using. Given an inequality like a > b write another inequality with the same meaning. Determine whether an inequality like –3 5 is true or false. Slide 24Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. The symbol means “is greater than.” Sentences using are inequalities.

25. EXAMPLE 9.2 The Real Numbers d Determine which of two real numbers is greater and indicate which, using. Given an inequality like a > b write another inequality with the same meaning. Determine whether an inequality like –3 5 is true or false. Slide 25Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.

26. 9.2 The Real Numbers ORDER; >, < Slide 26Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.

27. 9.2 The Real Numbers Slide 27Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.

28. 9.2 The Real Numbers d Determine which of two real numbers is greater and indicate which, using. Given an inequality like a > b write another inequality with the same meaning. Determine whether an inequality like –3 5 is true or false. Slide 28Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.

29. EXAMPLE 9.2 The Real Numbers d Determine which of two real numbers is greater and indicate which, using. Given an inequality like a > b write another inequality with the same meaning. Determine whether an inequality like –3 5 is true or false. Slide 29Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. Write true or false for each statement.

30. 9.2 The Real Numbers ABSOLUTE VALUE Slide 30Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. The absolute value of a number is its distance from zero on the number line. We use the symbol to represent the absolute value of a number x.

31. 9.2 The Real Numbers Slide 31Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. a) If a number is negative, its absolute value is its opposite. b) If a number is positive or zero, its absolute value is the same as the number.

32. EXAMPLE 9.2 The Real Numbers e Find the absolute value of a real number. Slide 32Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. Find the absolute value.