Section 1.1 Introduction to Algebra and the Set of Real Numbers 53 5. Absolute Value of a Real Number The concept of absolute value will be used to define the addition of real numbers in Section 1.3. Informal Definition of the Absolute Value of a Real Number The absolute value of a real number a, denoted 0a 0, is the distance between a and 0 on the number line. Note: The absolute value of any real number is positive or zero. For example, 03 0 3 and 03 0 3. 3 units 3 units ��6 ��5 ��4 ��3 ��2 ��1 0 1 2 3 4 5 6 Finding the Absolute Value of a Real Number Example 9 Evaluate the absolute value expressions. a. b. c. d. Solution: a. is 4 units from 0 on the 00 0 06.2 0 012 04 0 0 04 0 4 4 number line. 12 0 12 0 1 2 12 b. is unit from 0 on the number line. 4 units 4 3 2 1 0 1 c. 06.2 0 6.2 6.2 is 6.2 units from 0 on the number line. Instructor Note: Remind students that because absolute value is a measure of distance it will always be nonnegative. We don’t measure distance with negative numbers. 00 0 0 6.2 units 7 6 5 4 3 2 1 0 1 d. 0 is 0 units from 0 on the number line. unit 12 0 units 3 2 1 0 1 2 The absolute value of a number a is its distance from 0 on the number line. 0a 0 The definition of may also be given symbolically depending on whether a is negative or nonnegative. Skill Practice Evaluate. 25. 26. 27. 01.4 0 28. 01 0 `7 8 099 0 ` Answers 25. 99 26. 27. 1.4 28. 1 7 8 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. 3 2 1 0 1 2 Classroom Examples: p. 58, Exercises 66 and 70
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