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Transcript
Chapter 2-7 The Real Number System The set of rational numbers and the set of irrational number together form the set of REAL NUMBERS. Natural Numbers = {1, 2, 3, …} Whole Numbers = {0, 1, 2, 3, …} Integers = {…, -2, -1, 0, 1, 2, …} Rational Numbers: a/b where b ≠ 0. The decimal form of a rational number is a terminating or repeating decimal. Irrational numbers: the decimal form of a irrational number is a non-terminating, nonrepeating decimal. Completeness Property for Points on the Number Line Distance between two points. Subtract lesser from the greater. Examples: Find distance (d) between -0.25 and 1/3 -1/4 and 1/3 -3/12 and 4/12 d = 4/12 - - 3/12 d = 4/12 + 3/12 d = 7/12 Find the distance (d) between п and -√8 (round to nearest hundredth) d = 3.14 - - 2.83 d = 3.14 + 2.83 d = 5.97 Find the distance (d) between √5 and √9 √5 = 2.24 √9 = 3 d = 3 – 2.24 d = 0.76 Continue on next page: Density Property of Real Numbers: between any two real numbers, there are other real numbers. Find the midpoint between each pair of numbers. To find the “Midpoint” add the two numbers than find their average (÷2) Example: 5.256 and 1 ½ Midpoint = 5.235 + 1.5 2 = 6.735/2 = 3.3675 (round to nearest thousandths if needed) = 3.368 Midpoint of 2 3/10 and 2.41 = 2.3 + 2.41 2 = 4.71 ÷ 2 = 2.355 Label each of the numbers as: natural numbers, whole numbers, integers, rational numbers, irrational numbers. Reminder: Natural Numbers = {1, 2, 3, …} Whole Numbers = {0, 1, 2, 3, …} Integers = {…, -2, -1, 0, 1, 2, …} Rational Numbers: a/b where b ≠ 0. The decimal form of a rational number is a terminating or repeating decimal. Irrational numbers: the decimal form of a irrational number is a non-terminating, nonrepeating decimal. Example: п is irrational -√144 is -12 which is: integer, rational number √90 is irrational 9.456456456….: rational - 6 3/5: rational 117/13 is 9: rational, integer, whole, natural.