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Published byAbigail Brooks Modified over 4 years ago

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**Making Sense of Rational and Irrational Numbers**

Objectives: Identify number sets. Write decimals as fractions. Write fractions as decimals.

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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. Irrational numbers Rational numbers Real Numbers Integers Whole numbers

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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

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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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**Biologists classify animals based on shared characteristics**

Biologists classify animals based on shared characteristics. The horned lizard is an animal, a reptile, a lizard, and a gecko. Rational Numbers are classified this way as well! 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

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**Venn Diagram: Naturals, Wholes, Integers, Rationals**

Real Numbers Rationals Integers Wholes Naturals

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

number belongs. Circle the most specific set. Integers , Rationals Rationals Naturals , Wholes , Integers , Rationals Wholes , Integers , Rationals Rationals

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Irrational numbers can 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 is irrational. A repeating decimal may not appear to repeat on a calculator, because calculators show a finite number of digits. Caution!

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Reminder Real numbers are all the positive, negative, fraction, and decimal numbers you have heard of. They are also called Rational Numbers. IRRATIONAL NUMBERS are usually decimals that do not terminate or repeat. They go on forever. Examples: π

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

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**Decimal to Fraction: A skill you will need for this unit!**

To change a decimal to a fraction, take the place value and reduce! 0.5 means 5 tenths, so 5/10. Now reduce 5/10 = ½ 0.5 = 1/2

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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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