REAL NUMBERS

(as opposed to fake numbers?)

Real Numbers

• Real Numbers are every number.

• Therefore, any number that you can find on the number line.

• Real Numbers have two categories.

What does it Mean?

• The number line goes on forever.• Every point on the line is a REAL

number.• There are no gaps on the number line.• Between the whole numbers and the

fractions there are numbers that are decimals but they don’t terminate and are not recurring decimals. They go on forever.

Real Numbers

REAL NUMBERS

-8 -5,632.1010101256849765…

61

49%

π

549.23789

154,769,852,354

1.333

WHOLENumber

s

REAL NUMBERS

IRRATIONALNumbers

NATURALNumbers

RATIONALNumbers

INTEGERS

Two Kinds of Real Numbers

• Rational Numbers

• Irrational Numbers

Irrational Numbers

•An irrational number is a number that cannot be written as a fraction of two integers.

•Irrational numbers written as decimals are non-terminating and non-repeating.

Examples of Irrational Numbers

• Pi ∏ 3.141592654

Rational Numbers

•A rational number is a real number that can be written as a fraction.

•A rational number written in decimal form is terminating or repeating.

Examples of Rational Numbers

•16•1/2•3.56

•-8•1.3333…

•- 3/4

Try this!

• a) Irrational

• b) Irrational

• c) Rational

• d) Rational

• e) Irrational66 e)

d)

25 c)

12 b)

2 a)

115

Integers

One of the subsets of rational numbers

What are integers?

• Integers are the whole numbers and their opposites.

• Examples of integers are 6-120186-934

• Integers are rational numbers because they can be written as fraction with 1 as the denominator.

Types of Integers

• Natural Numbers(N): Natural Numbers are counting numbers from 1,2,3,4,5,................N = {1,2,3,4,5,................}

• Whole Numbers (W): Whole numbers are natural numbers including zero. They are 0,1,2,3,4,5,...............W = {0,1,2,3,4,5,..............} W = 0 + N

WHOLENumber

s

REAL NUMBERS

IRRATIONALNumbers

NATURALNumbers

RATIONALNumbers

INTEGERS

What categories of Real Numbers do these

numbers belong in?

Comparing Rational and Irrational Numbers

• When comparing different forms of rational and irrational numbers, convert the numbers to the same form.

Compare -3 and -3.571 (convert -3 to -3.428571…

-3.428571… > -3.571

37

37

Practice

Ordering Rational and Irrational Numbers

• To order rational and irrational numbers, convert all of the numbers to the same form.

• You can also find the approximate locations of rational and irrational numbers on a number line.

Example• Order these numbers from least to

greatest. ¹/₄, 75%, .04, 10%, ⁹/₇

¹/₄ becomes 0.2575% becomes 0.750.04 stays 0.0410% becomes 0.10

⁹/₇ becomes 1.2857142…

Answer: 0.04, 10%, ¹/₄, 75%, ⁹/₇

Practice

Order these from least to greatest: