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Real Numbers

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Set: a collection of objects – like a group Terminating Number: a number that ends –Example: 4

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Repeating Number: a number that goes on forever WITH a pattern. –Example: 0.898889888988… Non-Terminating or Non-Repeating Number: a number that goes on forever without a pattern –Example:

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An easy way to remember the difference between rational and irrational…. RATIONAL The word RATIO is in the word rational. That’s because Rational Numbers are a ratio of two numbers. RATIO

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6 or 6 1 Can also be written as6.0 -2 1 Can also be written as-2.0 1212 Can also be written as0.5 -5 4 Can also be written as-1.25 2323 Can also be written as0.666666666... 21 55 Can also be written as0.38181818... 53 83 Can also be written as 0.62855421687... the decimals will repeat after 41 digits

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Real Numbers Real numbers are either Rational or Irrational

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DefinitionFacts/Characteristics ExampleNon-Example Irrational Numbers They are crazy! They go on forever without a pattern. Numbers that don’t repeat and don’t terminate. √2,.8798945…, ∏ ½, 2.35, -¼, -.3

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DefinitionFacts/Characteristics ExampleNon-Example Rational Numbers Numbers that terminate or repeat. √2,.8798945…, ∏ Rational is the most loving set of Real Numbers – they let everyone in. ½, 2.35, -¼, -.3

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Rational numbers can be broken down further into 3 sets of numbers: Natural Numbers (Counting Numbers) Whole Numbers Integers Sets of Real Numbers

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DefinitionFacts/Characteristics ExampleNon-Example Integers ½, 2.35, -¼, -.3 …-2, -1, 0, 1, 2… Positive & negative whole numbers, including zero. Integers are like whole numbers, except they include negatives.

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DefinitionFacts/Characteristics Example Non-Example Whole Numbers Positive numbers and zero that do not have fractions or decimals. Whole numbers have zero because they have an ‘o’ 0, 1, 2, 3, 4… -3, -4.3, ½, 2.35

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DefinitionFacts/Characteristics ExampleNon-Example Natural Numbers Positive numbers that are used to count. Smallest most restrictive set. 1, 2, 3, 4, 5… 0, -3, ½, 2.35

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Real Numbers Diagram

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Real Numbers Flow Chart

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