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Rational and Irrational Numbers

Rational and Irrational Numbers. Monday, September 27 th , 2010. The set of real numbers consists of the set of rational numbers and the set of irrational numbers. Real Numbers. Rational numbers. Irrational numbers. Integers. Whole numbers.

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Rational and Irrational Numbers

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  1. Rational and Irrational Numbers Monday, September 27th, 2010

  2. The set of real numbers consists of the set of rational numbers and the set of irrational numbers. Real Numbers Rational numbers Irrational numbers Integers Whole numbers

  3. RATIONAL NUMBERSDefinition: written as fractions, and as decimals that either terminate or repeat. • Rational numbers are nice and neat! • Fractions • Terminating Decimals • Repeating Decimals 21.89 • Whole Numbers • Integers • Perfect Squares 3.8 0.6 0 -4 144 = 12

  4. 2 ≈1.414213562373095048… 73 ≈8.54400374531753116… Irrational NumbersDefinition:can only be written as decimals that do not terminate or repeat. • Irrational numbers are crazy numbers! • Non-terminating and Non- repeating Decimals (go on and on and on but don’t repeat) 65.65971059893… 0.363765489965… • Non- Perfect Squares • HINT: If a whole number is not a perfect square, then its square root is an irrational number.

  5. Classify as rational or irrational and WHY??: • 5 • –12.75 • 16 2

  6. Classify as rational or irrational and WHY??: 9 = 3 9 3 81 3 = = 3 9 4. rational –35.9 –35.9 is a terminating decimal. 5. rational 81 3 6. rational

  7. Non-Real Numbers • Radicals ( ) can’t have a negative number • If there is a negative inside the radical, then it is a NON-REAL NUMBER • 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

  8. Mini Quiz 4 • 9 3 4 3 8 Find a real number between –2 and –2 . 5 8 Possible answer –2 . Write all names that apply to each number (real, non-real number, irrational, rational) 16 2 2. – 1. 2 real, irrational real, integer, rational State if each number is rational, irrational, or not a real number. 25 0 4. 3. rational not a real number 5.

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