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: 0.898889888988…

•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….

RATIONALThe 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 6.0

-21

Can also be written as -2.0

12

Can also be written as 0.5

-54

Can also be written as -1.25

23

Can also be written as 0.666666666...

2155

Can also be written as 0.38181818...

5383

Can also be written as0.62855421687...

the decimals will repeatafter 41 digits

Real Numbers

• Real numbers are either Rational or Irrational

Definition Facts/Characteristics

Example Non-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

Definition Facts/Characteristics

Example Non-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

Rational numbers can be broken down further into 3 sets of numbers: Natural Numbers (Counting

Numbers) Whole Numbers Integers

Sets of Real Numbers

Definition Facts/Characteristics

Example Non-ExampleIntegers

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.

Definition Facts/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

Definition Facts/Characteristics

Example Non-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