1. Real Numbers System

2. REAL NUMBERS can be broken down into the
following groupings:
Natural Numbers
Whole Numbers
Integers
Rational Numbers
Irrational Numbers

3. Natural Numbers Are counting numbers
They are numbers that are seen “naturally in nature”
They DO NOT include zero, since zero is not a naturally occurring concept
The Natural Numbers category has the LEAST amount of numbers in it
Examples:

4. Whole Numbers Are all natural numbers INCLUDING zero
Whole numbers DO NOT include partial numbers (decimals/fractions) or negative numbers
This category is very similar to natural numbers, except it includes zero
Examples:

5. Integers Are all positive and negative whole numbers including zero
Integers are just like the category of whole numbers (since they include positive whole numbers and zero), but they also include negative numbers
Think of a number line!!!!
Examples:

6. Rational Numbers
Are all numbers that can be expressed in fraction form (a/b) where “a” and “b” are integers and “b” CANNOT be equal to zero
Rational numbers include repeating decimals (patterns) and terminating decimals (decimals that end)
Examples:

7. IRRATIONAL NUMBERS
These are a new category that we are introducing today.
Are numbers that can ONLY be represented by:
Non-repeating
Non-terminating decimals
This is a category all to itself as it DOES NOT include ANY numbers that can be placed in the natural, whole, integer or rational numbers categories
These numbers CANNOT be represented as fractions
Examples:

9. Examples of the
Real Numbers
System: