8 Chapter 1 Real Numbers and Algebraic Expressions Procedure: Graphing a Point on a Number Line Step 1: Locate the number on the number line. a. If the number is a fraction, convert it to a decimal value. b. If the number is irrational, approximate its value to two decimal places. Step 2: Draw a dot on its position on the number line. Objective 3 Examples Graph the numbers -3.2, -4 Objective 4 ▶ Find the opposite of a real number. 1 2 , 19, 115, 0, -6, and 3 4 on a number line. Solution If the number is not an integer, round it to the nearest hundredth to approximate its value and to find its location on the number line. -4 1 2 =-4.50, 115 ≈ 3.87, 3 4 = 0.75 –6 –3.2 0 √−9 34 1 2 3 4 5 6 –412 √⎯15 –6 –5 –4 –3 –2 –1 0 Student Check 3 Graph the numbers -5.4, -2 1 4 , 116, 13, -3, and 2 5 on a number line. Opposites Two numbers that lie equal distances from zero are opposites of one another. Definition: The opposite of a real number a is the number that has the same distance from 0 on a number line but lies on the opposite side of 0 from a. The opposite of a real number a is denoted as -a. –6 –5 –4 –3 –2 –1 0 1 2 3 4 5 6 3 units 3 units The number line illustrates that -3 and 3 are opposites of one another since they are the same distance from zero and on opposite sides of zero. These numbers are also referred to as additive inverses. Verbal Statement Mathematical Statement The opposite of 3 is -3. -(3) = -3 The opposite of -3 is 3. -(-3) = 3 Note: • The opposite of a positive real number is a negative number. • The opposite of a negative real number is a positive number.
hendricks_intermediate_algebra_1e_ch1_3
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