Real Numbers 6 Chapter 1 Real Numbers and Algebraic Expressions Rational Numbers Whole Numbers 0 This diagram illustrates the following facts. • The set of natural numbers is a subset of the set of whole numbers, the set of integers, and the set of rational numbers—that is, ⊂ , ⊂ , ⊂ . • The set of whole numbers is a subset of the set of integers and the set of rational numbers—that is, ⊂ , ⊂ . • The set of integers is a subset of the set of rational numbers—that is, ⊂ . • The set of rational numbers together with the irrational numbers make up the real numbers—that is, ∪ = . • A rational number cannot be an irrational number—that is, = . In Chapter 8, another set of numbers, called the complex numbers, is introduced. This set actually contains all of the real numbers. Procedure: Classifying a Real Number as a Natural Number, Whole Number, Integer, Rational Number, or Irrational Number Step 1: If the number is 1, 2, 3, . . . , then the number is a natural number. Step 2: If the number is 0, 1, 2, 3, . . . , then the number is a whole number. Step 3: If the number is . . . , -3, -2, -1, 0, 1, 2, 3, . . . , then the number is an integer. Step 4: Determine if the number is rational or irrational. a. If the number is equivalent to a decimal that terminates or repeats, then it is rational. b. If the number is equivalent to a decimal that doesn’t terminate or repeat, then it is irrational. Objective 2 Examples Classify each number in the set 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 the form of a fraction. If the number is irrational, approximate its value to two decimal places. 2a. e 3.2, -4 1 2 , 19, 115, 0, -8, 3 4 f Irrational Numbers p = 3.14159 √−. . . 5 e = 2.71828 . . . 5.616116111 . . . Integers –3 –2 –1 25 7 0.25 0.9292 . . . 11 – Natural Numbers 1 2 3
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