Section 1.1 The Set of Real Numbers 7 To determine how the numbers -10 and -20, for example, relate to one another, we will use a thermometer. As we move up a thermometer, the temperatures get larger. As we move down a thermometer, the temperatures get smaller. Since -20 lies below -10 on the thermometer, -20 is less than -10. That is, -20 < -10. When the thermometer, or number line, is rotated horizontally, we see that -20 is to the left of -10. –30–20–10 0 10 20 30 40 50 60 60 50 40 30 20 10 0 –10 –20 –30 �������������������� Order of Real Numbers If a number a lies to the left of a number b on a real number line, then a < b or a ≤ b. If a number a lies to the right of a number b on a real number line, then a > b or a ≥ b. If a number a lies in the same location as a number b on a real number line, then a = b. �� ������������������������ ������������������ Use the number line to compare the numbers. Use a <, >, or = symbol to make a true statement. Problems Solutions 3a. -3 -4 –5 –4 –3 –2 –1 0 1 -3 lies to the right of -4 ⇒ -3 > -4. 3b. -2 0 –5 –4 –3 –2 –1 0 1 -2 lies to the left of 0 ⇒ -2 < 0. 3c. π 15 Note that π ≈ 3.14 and 15 ≈ 2.24. √5− p 0 1 2 3 4 5 6 π lies to the right of 15 ⇒ π >15. 3d. 3.5 7 2 Note that 7 2 = 3.5. The two numbers are equal, so 3.5 = 7 2 . Student Check 3 Use the number line to compare the numbers. Use a <, >, or = symbol to make a true statement. a. -5 -4 b. 12 1 2 c. 1.25 5 4 ���������� The inequality statements in Example 3 can also be written by reversing the inequality symbol. In either case, the arrow points to the smaller number. The statement -3 > -4 can also be written as -4 < -3. The statement -2 < 0 can also be written as 0 > -2. The statement π > 15 can also be written as 15 < π.
hendricks_beginning_algebra_1e_ch1_3
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