Warm UpAdd or subtract.

1 + – 1 5 11. 2

5

2. 7 123 – 2

3. 6.5 + –1.2

4. 3.4 – 0.9

5.3

2.5

3 5

11 12

1 3 1

The Real Number System

The Real Number System• A real number is basically a number

that is somewhere on a number line.• The Real Number System is divided into

two categories: Rational and Irrational.

A rational number is any number that can be written as a fraction , where n

and d are integers and d 0.

nd

• Fractions are rational numbers.• Decimals that terminate or repeat

are rational numbers.• Whole numbers are rational

numbers.• Integers are rational numbers.• 0 is a rational number.

An Irrational Number is a number that cannot be written as a simple fraction - the decimal goes on forever without repeating.

It is called irrational because it cannot be written

as a ratio (or fraction),not because it’s crazy!

• π (Pi) is an irrational number. The value of Pi is

3.141592653589793238462643383279 (and more...)

• There is no pattern to the decimals, and you cannot write down a simple fraction that equals Pi.

• Square roots of non-perfect “squares” are irrational.

• For example,

is irrational.

• Real numbers consist of all the rational and irrational numbers.

• The real number system has many subsets:– Natural Numbers – Whole Numbers – Integers

• Natural numbers are the set of counting numbers.

{1, 2, 3,…}

• Whole numbers are the set of numbers that include 0 plus the set of natural numbers.

{0, 1, 2, 3, 4, 5,…}

• Integers are the set of whole numbers and their opposites.

{…,-3, -2, -1, 0, 1, 2, 3,…}

Real Numbers

Rational Numbers Irrational Numbers

3

1/2-2

15%

2/3

1.456

-0.7

0

3 2

5 2

34

Real Numbers

Rational Numbers Irrational Numbers

31/2

-2

15%

2/3

1.456- 0.7

3 2

5 2

34

Integers

Real Numbers

Rational Numbers Irrational Numbers

31/2

-2

15%

2/3

1.456- 0.7

3 2

5 2

34

Integers

Whole

Real Numbers

Rational Numbers Irrational Numbers

31/2

-2

15%

2/3

1.456- 0.7

0

3 2

5 2

34

Integers

Whole

Natural

System

• Where do these numbers belong?0, ½, -3, , 117, 6.36, .3,

0

117-3

1/2

6.36

.3

System