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Rational and Irrational Numbers Monday, September 27th, 2010 The set of real numbers consists of the set of rational numbers and the set of irrational numbers. Real Numbers Rational numbers Integers Whole numbers Irrational numbers RATIONAL NUMBERS Definition: written as fractions, and as decimals that either terminate or repeat. Rational numbers are nice and neat! 2 1. Fractions 3 2. Terminating Decimals 3. Repeating Decimals 4. Whole Numbers 5. Integers 3.8 0.6 0 -4 6. Perfect Squares 144 = 12 21.89 Irrational Numbers Definition: can only be written as decimals that do not terminate or repeat. Irrational numbers are crazy numbers! 1. Non-terminating and Non- repeating Decimals (go on and on and on but don’t repeat) 65.65971059893… 0.363765489965… 2. Non- Perfect Squares 73 ≈8.54400374531753116… 2 ≈1.414213562373095048… HINT: If a whole number is not a perfect square, then its square root is an irrational number. Classify as rational or irrational and WHY??: 1. 5 2. –12.75 3. 16 2 Classify as rational or irrational and WHY??: 4. 9 =3 9 rational 5. –35.9 –35.9 is a terminating decimal. rational 6. 81 3 rational 81 = 9 = 3 3 3 Non-Real Numbers 1. Radicals ( ) can’t have a negative number – If there is a negative inside the radical, then it is a NON-REAL NUMBER 2. 0 can’t be in the denominator of a fraction Example: -9 -18 -49 These are ok (the negative is outside of the - 100 81 - 49 ): Mini Quiz Write all names that apply to each number (real, non-real number, irrational, rational) 1. 2 2. – real, irrational 16 2 real, integer, rational State if each number is rational, irrational, or not a real number. 3. 25 0 not a real number 4. 4 • 9 rational 3 3 Find a real number between –2 and –2 . 5. 4 8 5 Possible answer –28 .