Section 1.1 The Set of Real Numbers 5 �� ������������������������ ������������������ Classify each number as a natural number, whole number, integer, rational number, irrational number, and/or real number. If the number is a rational number, write it in fractional form. If the number is irrational, approximate its value to two decimal places. 1a. 0.75 1b. -3 1 2 1c. 111 1d. 0 1e. 125 1f. 11 16 1g. -7 Solutions Number Natural Whole Integer Rational Irrational Real 1a. 0.75 = 75 100 = 3 4 X X 1b. -3 1 2 =- 7 2 X X 1c. 111 = 3.316624 . . . ≈ 3.32 X X 1d. 0 = 0 1 X X X X 1e. 125 = 5 = 5 1 X X X X X 1f. 11 16 X X 1g. -7=- 7 1 X X X Student Check 1 Classify each number as a natural number, whole number, integer, rational number, irrational number, and/or real number. If the number is a rational number, write it in fractional form. If the number is irrational, approximate its value to two decimal places. a. 0.4 b. -6 4 7 c. 136 d. 10 e. 121 f. 5 6 g. -5 h. 1.232232223 . . . The Real Number Line Graphing or plotting real numbers on a number line is a skill that will be used in later sections when we solve inequalities and graph equations. The act of reading a thermometer can assist us in plotting real numbers. Figure 1.1 illustrates a thermometer reading of 70°F and Figure 1.2 illustrates a thermometer reading of -10°F. If we rotate the thermometer, we get a number line. If we put a dot at 70°F, we have graphed the real number 70. If we put a dot at -10°F, we have graphed the real number -10, as shown. 70 80 70 60 50 40 30 20 10 0°F –10 –20 –30 –40 –10 80 70 60 50 40 30 20 10 0°F –10 –20 –30 –40 The real number line is similar to this rotated thermometer. It is a horizontal line drawn with arrows on both ends to indicate that the real numbers are infinite. Tick marks are used to divide the number line into equal segments. Positive numbers are Objective 2 ▶ Graph real numbers on a real number line. 80 70 60 50 40 30 20 10 0°F –10 –20 –30 –40 �������������������� 80 70 60 50 40 30 20 10 0°F –10 –20 –30 –40 ��������������������
hendricks_beginning_algebra_1e_ch1_3
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