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Subunit A1: The Real Numbers

 

CLASSIFICATION OF REAL NUMBERS - CONTINUED

7. By now you’re probably thinking that there can’t possibly be any other types of numbers. Wrong! We still need to consider the set of numbers that are NOT Rational. Since the prefix “ir” means “not” we call this set of numbers Irrational.

• By definition, the Irrational Numbers are the set of non-terminating, non-repeating decimal numbers.

• Or we could say that the Irrational Numbers are those real numbers that are not rational.

• Examples of Irrational Numbers include such numbers as:

▪ –Ö7 » 2.645751311064590590501 ...

[In fact the square root of any prime number is irrational.],

▪ π » 3.14159265358979323846264 …

[This Greek letter, known as pi, is represents the number that results from dividing the circumference of any circle by its diameter.]

▪ e » 2.71828182845904523536028 …

[This is the constant known as Euler’s number and is the base of the natural logarithms.]

Lesson 1.1: Real Numbers -- The Real Numbers

Lesson Overview

8 Of 10

Real Numbers - DD09.
Real Numbers - DD07.
Discussion/Demo.
Guided Practice.
Independent Practice.
Summary.
Self Check.

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Natural Numbers

{1, 2, 3, 4, ...}

Zero

{0}

Whole Numbers

 

{0, 1, 2, 3, 4, ...}

Opposites of Natural Numbers

{... ,-4, -3, -2, -1}

Integers

{... -2, -1, 0, 1, 2, ...}

Non-Integral

Rationals

Ex: -5.7, -¼, ½, 3⅞

Irrational Numbers

{... -2, -1, 0, 1, 2, ...}

Rational Numbers

Ex: -2, -¾, 0, 4.6, 8⅞