Real Numbers

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

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

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

6 or 6 1 Can also be written as Can also be written as Can also be written as Can also be written as Can also be written as Can also be written as Can also be written as the decimals will repeat after 41 digits

Real Numbers Real numbers are either Rational or Irrational

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, …, ∏ ½, 2.35, -¼, -.3

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

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

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.

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

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

Real Numbers Diagram

Real Numbers Flow Chart