Real Numbers System

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

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:

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:

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:

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:

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:

Examples of the Real Numbers System: