1. Mrs.Volynskaya Real Numbers

2. 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, , 4/5,
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 ???

3. WORLD OF REAL NUMBERS

4. EXAMPLE
Classify all the following numbers as natural, whole, integer, rational, or irrational. List all that apply.
117 … -½
6.36
1/9 -3

8. EXAMPLE -3 is an integer and a rational number.
77 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.
… 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.

9. Set
A collection of objects.
Set Notation
{ }
Natural
numbers
Counting numbers {1,2,3, …}
Whole
Numbers
Natural numbers and 0.
{0,1,2,3, …}
Integers
Positive and negative natural numbers and zero. {… -2, -1, 0, 1, 2, 3, …}
Rational
Number
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.

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
Copyright © 2011 Pearson Education, Inc.

11. Copyright © 2011 Pearson Education, Inc.
To which set of numbers does 6 belong?
a) Natural Numbers
b) Whole numbers
c) Integers
d) Rational numbers
e) Irrational numbers
f) Real numbers
Copyright © 2011 Pearson Education, Inc.

12. Definitions A symbol that can vary in value. Variable
A symbol that does not vary in value.
Constant
A mathematical relationship that does not contain an equal sign
Expression
A mathematical relationship that contains an equal sign.
Equation
A mathematical relationship that contains an inequality symbol (, <, >, , or ).
Inequality
Vocabulary Matching Cards
Absolute Value
A given number’s distance from 0 on a number line. Notation = | |.