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

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**Making Sense of Rational and Irrational Numbers**

Essential Question: How are rational and irrational numbers simplified?

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**Numbers can also be classified!**

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

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**It consists of 2 subsets – rational numbers and irrational numbers.**

The set of real numbers is all numbers that can be written on a number line. It consists of 2 subsets – rational numbers and irrational numbers. Irrational numbers Rational numbers Real Numbers Integers Whole numbers

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**Rational Numbers Natural Numbers - Natural counting 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. Ex: -0.76, -6/13, 0.08, 2/3

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**Name all the sets of numbers to which the given**

number belongs. Circle the most specific set. Integer , Rational Rational Naturals , Whole , Integer , Rational Whole , Integer , Rational Rational

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Venn Diagram Real Numbers Rational Integer Whole Natural

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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

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**Classify the Following:**

Irrational … Rational (equals -⅓)

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**Classify the Following:**

… Irrational (no end, no repetition) 1⅔ Rational (can be 5/3 ) Rational (equals 10 or 10/1 )

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**Rational v. Irrational – How alike?**

Subsets of Real numbers Can be negative Can be non-terminating (never end)

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**Rational v. Irrational – How different?**

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

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Irrational numbers can be written only as decimals that do not 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. A repeating decimal may not appear to repeat on a calculator, because calculators show a limited number of digits! Caution!

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**Identify each root as rational or irrational.**

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**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

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**Converting Fractions and Decimals**

To change a fraction to a decimal, take the top divided by the bottom, or numerator divided by the denominator.

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Complete the table. Fraction Decimal

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

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Repeating Decimals Fraction Decimal

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Repeating Decimals Fraction Decimal

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**Rational Numbers CAN be made into a fraction a/b, where b ≠ 0.**

A repeating OR terminating decimal. 2/3 …

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**Irrational Numbers CANNOT be made into a fraction a/b, where b ≠ 0.**

A non-repeating AND non-terminating decimal number. π …

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