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8/27/15

8/27/15. Please complete the “ conclusion ” questions on the back of your scavenger hunt. Share with a neighbor. Let ’ s share out. Making Sense of Rational and Irrational Numbers. Essential Question: How are rational and irrational numbers simplified?.

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8/27/15

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  1. 8/27/15 • Please complete the “conclusion” questions on the back of your scavenger hunt. • Share with a neighbor. • Let’s share out.

  2. Making Sense of Rational and Irrational Numbers Essential Question: How are rational and irrational numbers simplified?

  3. Biologists classify animals based on sharedcharacteristics. The horned lizard is an animal, a reptile, a lizard, and a gecko! Animal Reptile Lizard Numbers can also be classified! Gecko

  4. 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 2 subsets – rational numbers andirrational numbers.

  5. Rational Numbers Natural counting numbers. Natural Numbers - 1, 2, 3, 4 … Whole Numbers - Natural counting numbers and zero. 0, 1, 2, 3 … Integers - Whole numbers and their opposites. … -3, -2, -1, 0, 1, 2, 3 … Rational Numbers - Integers, fractions, and decimals. -0.76, -6/13, 0.08, 2/3 Ex:

  6. Name all the sets of numbers to which the given number belongs. Circle the most specific set. , Rational Integer Rational Naturals , Integer , Rational , Whole , Rational Whole , Integer Rational

  7. Venn Diagram Real Numbers Rational Integer Whole Natural

  8. Remember… Rational numbers can be written as a fraction or… as either a terminating or repeating decimal. 4 5 23 3 = 3.8 = 0.6 1.44 = 1.2

  9. Classify the Following: • Irrational • -0.33333… • Rational (equals -⅓)

  10. Classify the Following: • 0.818811888111… • Irrational (no end, no repetition) • 1⅔ • Rational (can be 5/3 ) • Rational (equals 10 or 10/1 )

  11. Rational v. Irrational – How alike? • Subsets of Real numbers • Can be negative • Can be non-terminating (never end)

  12. Rational v. Irrational – How different? • Rational: • CAN be a fraction • HAS a perfect square root • Can be terminating or repeating decimals • Irrational: • CANNOT be a fraction • Has NO perfect square root • Can only be non-terminating, non-repeating decimals

  13. Caution! A repeating decimal may not appear to repeat on a calculator, because calculators show a limited number of digits! Irrational numberscan be written only as decimals that donot terminate or repeat. They cannot be written as a fraction. 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 is irrational.

  14. Identify each root as rational or irrational.

  15. Decimal to Fraction: A skill you need for this unit! • To change a decimal to a fraction, take the place value and simplify! • 0.5 means “5 tenths,” so start with 5/10 • Now simplify 5/10 to ½ • So… 0.5 = ½

  16. Converting Fractions and Decimals Fraction Decimal To change a fraction to a decimal, take the top divided by the bottom, or numerator divided by the denominator.

  17. Complete the table. Fraction Decimal

  18. Repeating Decimals Fraction Decimal Every rational number (fraction) either terminates OR repeatswhen written as a decimal.

  19. Repeating Decimals Fraction Decimal

  20. Repeating Decimals Fraction Decimal

  21. Rational Numbers • CANbe made into a fraction a/b, where b ≠ 0. • A repeating OR terminating decimal. • 2/3 • 0.798798798…

  22. Irrational Numbers • CANNOTbe made into a fraction a/b, where b ≠ 0. • A non-repeating AND non-terminating decimal number. • π • 0.313311333111…

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