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Real Number System

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Real Numbers
Mrs.Volynskaya
Real Number System
-18, -1/2, 0, sqrt 2, pi, 47/10
Irrational Numbers
pi, sqrt 7
Rational Numbers
-35, -7/8, 0, 5, 27/11
Noninteger Rational Numbers
-14/5, 9/10, 30,13
Integers
-10, 0, 8
Negative Integers
-20, -13, -1
Whole Numbers
0, 2, 56, 198
Zero
0
Natural Numbers or
Positive Integers
1, 16, 170
•
•
•
•
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. в€љ2, в€љ3, в€љ5 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. 117
b. 0
c. -12.64039…
d. -ВЅ
e. 6.36
f. 1/9
g. -3
EXAMPLE
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.
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
Set Notation
Natural
numbers
Whole
Numbers
Integers
A collection of objects.
{ }
Counting numbers {1,2,3, …}
Natural numbers and 0.
{0,1,2,3, …}
Positive and negative natural numbers
and zero. {… -2, -1, 0, 1, 2, 3, …}
A real number that can be expressed
Rational
as a ratio of integers (fraction)
Number
Any real number that is not rational.
Irrational
пЂЁ 2 ,пЃ° пЂ©
Number
Real Numbers All numbers associated with
the number line.
To which set(s) of numbers does пЂ­6
belong?
a) Natural Numbers
b) Whole numbers
c) Integers
d) Rational numbers
e) Irrational numbers
f) Real numbers
Slide 1- 10
Copyright В© 2011 Pearson Education, Inc.
To which set of numbers does пЂ­6
belong?
a) Natural Numbers
b) Whole numbers
c) Integers
d) Rational numbers
e) Irrational numbers
f) Real numbers
Slide 1- 11
Copyright В© 2011 Pearson Education, Inc.
Definitions
Variable
A symbol that can vary in value.
Constant
A symbol that does not vary in
value.
A mathematical relationship that
does not contain an equal sign
Expression
Equation
A mathematical relationship that
contains an equal sign.
Inequality
A mathematical relationship that
contains an inequality symbol (п‚№, <,
>, п‚Ј, or п‚і).
Absolute Value
A given number’s distance from 0
on a number line. Notation = | |.
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