30 Chapter 1 The Set of Real Numbers 0a 0 Absolute Value of a Real Number Let a be a real number.Then 1. If a is nonnegative (that is, then 2. If a is negative (that is, a 6 02, then 0a 0 a. a 02, 0a 0 a. 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 Example 10 Determine if the statements are true or false. a. b. Solution: a. Simplify the absolute value. True 03 0 3 0 5 0 05 0 03 0 ? 03 0 3 3 3 ? 3 0 5 0 05 0 05 0 05 0 b. Simplify the absolute values. False 5 5 Skill Practice Answer true or false. 26. 0 4 0 7 04 0 27. 017 0 17 Answers 26. False 27. True The absolute value of a number a is its distance from 0 on the number line.The definition of may also be given symbolically depending on whether a is negative or nonnegative. 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 1.732050808 Calculator Connections
miller_beginning_intermediate_algebra_4e_ch1_3
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