Mrs.Volynskaya Real Numbers

Ir ra tion a l N u m be rsp i, sq r t 7

N o n in te g er R a tion a l N um be rs-1 4 /5 , 9 /1 0 , 30 ,13

N eg a tiv e In te ge rs-2 0 , -1 3 , -1

Z e ro0

N a tu ra l N u m b e rs o rP os it iv e In te ge rs

1 , 16 , 1 70

W h o le N u m b e rs0 , 2 , 5 6 , 1 98

In te ge rs-1 0 , 0 , 8

R a tio n a l N u m b e rs-3 5 , -7 /8 , 0 , 5 , 27 /11

R e a l N u m b e r S ys tem-1 8 , -1 /2 , 0 , sq r t 2 , p i , 47 /10

• The Set of Natural Numbers: {1, 2, 3,…}• The Set of Whole Numbers: {0, 1, 2, …}• The Set of Integers {… -3, -2, -1,0,1,2…}• Rational numbers can be written as

fractions or as decimals that either terminate or repeat: 2/7, 0.354, 3.555..., 4/5, 9.078302

• Irrational numbers can only be written as decimals that do not terminate or repeat. If a whole number is not a perfect square, then its square root is an irrational number. √2, √3, √5 are Irrational

• How about √1, √4 , √9, √16 ???

WORLD OF REAL NUMBERS

EXAMPLE• Classify all the following numbers as natural, whole, integer, rational, or irrational. List all that apply.a. 117b. 0c. -12.64039…d. -½e. 6.36f. 1/9 g. -3

EXAMPLE77 is a Natural number, a Whole number, an Integer, and a

Rational number.

9/10 is a rational number.

(- 5) is an integer, and a rational number.

17.5407… is an irrational number.

-3 is an integer and a rational number.5.39 is a rational number.– is an irrational number. 1/7 is a rational number.

Set A collection of objects.

Set Notation { }

Natural numbers

Counting numbers {1,2,3, …}

Whole Numbers

Natural numbers and 0.{0,1,2,3, …}

Rational Number

Integers Positive and negative natural numbers and zero. {… -2, -1, 0, 1, 2, 3, …}

A real number that can be expressed as a ratio of integers (fraction)

Irrational Number

Any real number that is not rational.

Real Numbers All numbers associated with the number line.

,2

Slide 1- 10 Copyright © 2011 Pearson Education, Inc.

To which set(s) of numbers does 6 belong?

a) Natural Numbers

b) Whole numbers

c) Integers

d) Rational numbers

e) Irrational numbers

f) Real numbers

Slide 1- 11 Copyright © 2011 Pearson Education, Inc.

To which set of numbers does 6 belong? To which set of numbers does 6 belong?

a) Natural Numbersa) Natural Numbers

b) Whole numbersb) Whole numbers

c) Integersc) Integers

d) Rational numbersd) Rational numbers

e) Irrational numberse) Irrational numbers

f) Real numbers

Definitions

Variable A symbol that can vary in value.

Constant A symbol that does not vary in value.

Expression A mathematical relationship that does not contain an equal sign

Equation A mathematical relationship that contains an equal sign.

Inequality A mathematical relationship that contains an inequality symbol (, <, >, , or ).

Absolute Value A given number’s distance from 0 on a number line. Notation = | |.