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Unit 13 L-3 Math 8 Aim: To classify real numbers as rational or irrational and understand that every number has a decimal expansion (8.NS.1) Real Numbers Rational Numbers Integers, whole numbers, natural numbers Ratios, terminating and repeating decimals Irrational Numbers Examples: -5, 2/3, 4 1/4, -1/6, 0, 11, 7.288, 9.6666..., 0.512512.... Nonterminating, nonrepeating decimals π, 0.121221222..., square root of 3, square root of 8 Classifying Sets of Numbers Natural Numbers, or Counting Numbers {1, 2, 3, 4, ….} Whole Numbers – the set of Natural numbers plus zero: {0, 1, 2, 3, 4, ….} Integers – consists of Whole Numbers and their Opposites: {…-3, -2, -1, 0, 1, 2, 3 …} ! Rational Numbers – a number you can write as the ratio of two integers in the form ! , where b ≠ 0. Rational numbers can be represented as either repeating or terminating decimals. This set includes the integers, whole numbers, and natural numbers as well as fractions, terminating decimals, and repeating decimals. Irrational Numbers – numbers that are not rational and cannot be written as a ratio. Irrational numbers include non-terminating, non-repeating decimals like π, 2.141141114…, 3, or 5. 2014-2015