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For more material and information, please visit Tai Lieu Du Hoc at www.tailieuduhoc.org 1.5 Ordering and the Real Number Line The set of all real numbers, which includes all integers and all numbers with 2 values between them, such as 1.25, , 2 , etc., has a natural ordering, which 3 can be represented by the real number line: | For more material and information please visit Tai Lieu Du Hoc at www.tailieuduhoc.org 1.5 Ordering and the Real Number Line The set of all real numbers which includes all integers and all numbers with values between them such as 1.25 -3 V2 etc. has a natural ordering which can be represented by the real number line 3 _ . 1 rr - . -V5 -0.4 4 V2 2.6 . . 2 2 . . --1 H. - Ị- I.-.I I . I- -3-2-10 1 2 3 Every real number corresponds to a point on the real number line see examples shown above . The real number line is infinitely long in both directions. For any two numbers on the real number line the number to the left is less than the number to the right. For example -45 2 2 -1.75 42 5 2 7.1 Since 2 5 it is also true that 5 is greater than 2 which is written 5 2. If a number N is between 1.5 and 2 on the real number line you can express that fact as 1.5 N 2. 11 For more material and information please visit Tai Lieu Du Hoc at www.tailieuduhoc.org 1.6 Percent The term percent means per hundred or divided by one hundred. Therefore 43 43 140 0.43 300 300 3 0.5 100 0.005 30 To find out what 30 of 350 is you multiply 350 by either 0.30 or 100 30 of 350 350 0.30 105 or 30 3 I 0 50 30 of 350 350 I 100 350 10 I 10 105. To find out what percent of 80 is 5 you set up the following equation and solve for x 5 _ x 80 _ 100 _ 500 _ x - 80 - 6 25 So 5 is 6.25 of 80. The number 80 is called the base of the percent. Another way to view this problem is to simply divide 5 by the base 80 and then multiply the result by 100 to get the percent. If a quantity increases from 600 to 750 then the percent increase is found by dividing the amount of increase 150 by the base 600 which is the first or the smaller of the two given numbers and then multiplying by 100 C60o 100 25 . If a quantity decreases from 500 to 400 then the percent decrease is found by dividing the amount of decrease 100 by the base 500 which is the first or the larger of the two given numbers and then multiplying by 100 100 100
