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Rational Vs. Irrational

Rational Vs. Irrational. Making sense of rational and Irrational numbers. Biologists classify animals based on shared characteristics. The horned lizard is an animal, a reptile, a lizard, and a gecko.

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Rational Vs. Irrational

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  1. Rational Vs. Irrational Making sense of rational and Irrational numbers

  2. Biologists classify animals based on shared characteristics. The horned lizard is an animal, a reptile, a lizard, and a gecko. You already know that some numbers can be classified as whole numbers, integers, or rational numbers. The number 2 is a whole number, an integer, and a rational number. It is also a real number. Animal Reptile Lizard Gecko

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

  4. Recall that rational numbers can be written as the quotient of two integers (a fraction) or as either terminating or repeating decimals. 4 5 23 3 = 3.8 = 0.6 1.44 = 1.2

  5. Irrational numberscan be written only as decimals that do not terminate or repeat. They 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.

  6. 16 2 4 2 = = 2 Additional Example 1: Classifying Real Numbers Write all classifications that apply to each number. A. 5 is a whole number that is not a perfect square. 5 irrational, real B. –12.75 –12.75 is a terminating decimal. rational, real 16 2 C. whole, integer, rational, real

  7. 9 = 3 81 3 9 3 = = 3 Check It Out! Example 1 Write all classifications that apply to each number. 9 A. whole, integer, rational, real –35.9 –35.9 is a terminating decimal. B. rational, real 81 3 C. whole, integer, rational, real

  8. A fraction with a denominator of 0 is undefined because you cannot divide by zero. So it is not a number at all.

  9. 0 3 = 0 Additional Example 2: Determining the Classification of All Numbers State if each number is rational, irrational, or not a real number. A. 21 irrational 0 3 B. rational

  10. Additional Example 2: Determining the Classification of All Numbers State if each number is rational, irrational, or not a real number. 4 0 C. not a real number

  11. Check It Out! Example 2 State if each number is rational, irrational, or not a real number. A. 23 is a whole number that is not a perfect square. 23 irrational 9 0 B. undefined, so not a real number

  12. 8 9 8 9 64 81 = Check It Out! Example 2 State if each number is rational, irrational, or not a real number. 64 81 C. rational

  13. 4 • 9 Lesson Quiz Write all classifications that apply to each number. 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

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