4 8 The Real Numbers Evaluating Algebraic Expressions

4 -8 The Real Numbers Evaluating Algebraic Expressions Rational and Irrational Numbers

4 -8 The Real Numbers Rational and Evaluating Algebraic Expressions Irrational Numbers Essential Question How do I distinguish between rational and irrational numbers?

4 -8 The Real Numbers Vocabulary Evaluating Algebraic Expressions real number irrational number

4 -8 The Real Numbers The set of real numbers is all numbers that can be written on a number line. It consists of the set Evaluating Algebraic Expressions of rational numbers and the set of irrational numbers. Real Numbers Rational numbers Integers Whole numbers Irrational numbers

4 -8 The Real Numbers Evaluating Algebraic Expressions Recall that rational numbers can be written as the quotient of two integers (a fraction) or as either terminating or repeating decimals. 3 4 = 3. 8 5 2 = 0. 6 3 1. 44 = 1. 2

4 -8 The Real Numbers Irrational numbers can be written only as decimals that do not terminate or repeat. They Evaluating Algebraic Expressions cannot be written as the quotient of two integers. If a whole number is not a perfect square, then its square root is an irrational number. For example, 2 is not a perfect square, so 2 is irrational. Caution! A repeating decimal may not appear to repeat on a calculator, because calculators show a finite number of digits.

4 -8 The Real Numbers Make a Venn Diagram that displays the following sets of numbers: Evaluating Algebraic Expressions Reals, Rationals, Irrationals, Integers, Wholes, and Naturals. Rationals -3 -2. 65 Integers -19 Wholes 0 Naturals 1, 2, 3. . . Reals Irrationals

4 -8 The Real Numbers Additional Example 1: Classifying Real Numbers Write all classifications that apply. Expressions to each number. Evaluating Algebraic A. 5 is a whole number that is not a perfect square. irrational, real 5 B. – 12. 75 is a terminating decimal. rational, real C. 16 2 16 4 = =2 2 2 whole, integer, rational, real

4 -8 The Real Numbers Check It Out! Example 1 Write. Evaluating all classifications that apply. Expressions to each number. Algebraic A. 9 9 =3 whole, integer, rational, real B. C. – 35. 9 is a terminating decimal. rational, real 81 81 9 = =3 3 whole, integer, rational, real

4 -8 The Real Numbers Evaluating Algebraic Expressions A fraction with a denominator of 0 is undefined because you cannot divide by zero. So it is not a number at all.

4 -8 The Real Numbers Additional Example 2: Determining the Classification of All Numbers Evaluating Algebraic Expressions State if each number is rational, irrational, or not a real number. A. 21 irrational B. 0 3 rational 0 =0 3

4 -8 The Real Numbers Additional Example 2: Determining the Classification of All Numbers Evaluating Algebraic Expressions State if each number is rational, irrational, or not a real number. C. 4 0 not a real number

4 -8 The Real Numbers Check It Out! Example 2 Evaluating Algebraic Expressions State if each number is rational, irrational, or not a real number. A. 23 23 is a whole number that is not a perfect square. irrational B. 9 0 undefined, so not a real number

4 -8 The Real Numbers Check It Out! Example 2 Evaluating Algebraic Expressions State if each number is rational, irrational, or not a real number. C. 64 81 rational 8 9 8 64 = 9 81