54 Chapter 1 The Set of Real Numbers 0a 0 This definition states that if a is a nonnegative number, then equals a itself. If a is a negative number, then equals the opposite of a. For example: 0a 0 09 0 9 09 0 Because 9 is positive, then equals the number 9 itself. Because is negative, then equals the opposite of , which is 7. 07 0 7 7 07 0 7 Comparing Absolute Value Expressions Determine if the statements are true or false. a. 03 0 3 b. 05 0 05 0 Solution: a. True. The symbol means “less than or equal to.” 03 0 03 0 03 0 3 Since is equal to 3, then 3 is a true statement. 05 0 05 0 05 0 05 0 b. False. On the left-hand side, is the opposite of . Hence 05 0 5. 05 0 5. On the right-hand side, Therefore, the original statement simplifies to 5 5, which is false. Example 10 Skill Practice Determine if the statements are true or false. 29. 04 0 7 04 0 30. 017 0 17 Classroom Examples: p. 58, Exercises 92 and 98 Answers 29. False 30. True Topic: Approximating Irrational Numbers on a Calculator Scientific and graphing calculators approximate irrational numbers by using rational numbers in the form of terminating decimals. For example, consider approximating and . Scientific Calculator: Enter: or Result: Enter: 3 Result: Graphing Calculator: Enter: Enter: 3 p 13 3.141592654 The symbol is read “is approximately equal to” and is used when writing approximations. Calculator Exercises Use a calculator to approximate the irrational numbers. Remember to use the appropriate symbol, , when expressing answers. 1. 112 2. 199 3. 4 p 4. 1p p 3.141592654 and 13 1.732050808 1.732050808 Calculator Connections 3.464101615 9.949874371 12.56637061 1.772453851
miller_introductory_algebra_3e_ch1_3
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