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Rational and Irrational Numbers

Rational and Irrational Numbers. Learning Target: Students can identify numbers as being rational or irrational. All REAL numbers are made up of RATIONAL & IRRATIONAL numbers…. Rational Numbers.

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Rational and Irrational Numbers

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  1. Rational and Irrational Numbers Learning Target: Students can identify numbers as being rational or irrational.

  2. All REAL numbers are made up of RATIONAL & IRRATIONAL numbers…

  3. Rational Numbers • A rational number is a number that can be written as a ratio. That means it can be written as a fraction, in which both the numerator (the number on top) and the denominator (the number on the bottom) are whole numbers. All rational numbers can be written as a fraction.

  4. Examples of Rational Numbers Rational Numbers are “Nice & Neat!” Fractions Terminating Decimals (stop / end) Repeating Decimals (decimal goes on forever) Whole Numbers Perfect Squares -6.23 17.1

  5. Irrational Numbers • All numbers that are not rational are considered irrational. An irrational number can be written as a decimal, but not as a fraction. Irrational numbers can NOT be written as a fraction!!

  6. Examples of Irrational Numbers Non-terminating and Non-repeating decimals (go on and on and on but don’t repeat) Non- Perfect Squares 0.363765489965… 65.65971059893… = 3.141592653589… = 3.141592653589… Irrational Numbers are “CRAZY!” ≈ 8.54400374531753116… ≈ 1.414213562373095048… ≈ 2.236067977499789696…

  7. Both rational and irrational numbers show up on the number line. This is why all “REAL” numbers include rational and irrational numbers.

  8. Non-Real Numbers • A non real number is a number that does not exist on a number line. They don’t show up on the number line!!

  9. Non-Real Numbers Imaginary Numbers: If there is a negative inside the radical, then it is a NON-REAL NUMBER = 5 Radicals can’t have a negative number (only ) Infinity: Infinity is the idea of something that has no end. ∞ -∞

  10. These are ok (the negative is outside of the radical)

  11. Real Numbers Non-Real Numbers

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