Number System Power Point

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Algebra 2 Numbers andFunctions

The Complex Number Systemand Oper ations with Number s



Repeating Decimals

� Repeating decimals are decimals that contain ainfinite number of digits.

� E xamples:

0.333«

7.689689«

FYI«The line above the decimals indicate that number

repeats.

9.1



Ter minating Decimals

� Ter minating decimals are decimals that contain afinite number of digits.

� E xamples:

36.8

0.125

4.5



The Complex Number System

Complex Number System

RealNumber s

Rational

Integer s

Whole Number s

Natur alNumber s

Irr ational

Imaginar yNumber s



Imaginar y Number s

Imaginar y number s are allthe number s that deal with the square r oot of a

negative number andcontain the letter i in it





Irr ational Number s

� Irrational numbers are any number s that cannotbe expressed as .

� They are expressed as non-terminating, non- repeating decimals; decimals that go on forever without repeating a patter n.

� E xamples of irr ational number s: ² 0.34334333433334« ² 45.86745893«

² (pi) ²

b

a

T

2



Rational Number s

� Rational numbers are any number s thatcan be expressed in the for m of , where a and b are integer s, and b � 0.

� They can always be expressed by usingter minating decimals or repeatingdecimals.

b

a



Integer s

� Integers are the set of whole number s andtheir opposites.

{«,-3, -2, -1, 0, 1, 2, 3,«}



Whole Number s

� Whole numbers are the set of number sthat include 0 plus the set of natur alnumber s.

{0, 1, 2, 3, 4, 5,«}



Natur al Number s

� Natural numbers are the set of countingnumber s.

{1, 2, 3,«}



Venn Diagr am of the Real Number System

Irrational NumbersRational Numbers



E xample

� Classify all the following number s as natural, whole,integer, rational, or irrational. List all that apply.

a. 117b. 0c. -12.64039«

d. -½e. 6.36f.g. -3

T



To show how these number are classified, use the Venn diagr am. Place the number where it belongs onthe Venn diagr am.

T

9

4

2

1

9

4

Rational Numbers

Integers

Whole Numbers

Natural

Numbers

Irrational Numbers

-12.64039«

117

0

6.36

-3



Solution

� Now that all the number s are placed where they belong inthe Venn diagr am, you can classify each number : ² 117 is a natur al number , a whole number , an integer ,

and a r ational number . ² is a r ational number . ² 0 is a whole number , an integer , and a r ational

number . ² -12.64039« is an irr ational number . ² -3 is an integer and a r ational number . ² 6.36 is a r ational number . ² is an i rr ational number .

² is a r ational number .

T

94

2

1



FYI«For Your Infor mation

� When taking the square r oot of any number that isnot a per fect square, the

resulting decimal will be non-ter minating and non-repeating. Therefore,those number s are always

irr ational.





Examples of Properties

Name the property displayed:

1. -2 + ( x ² 5) = (-2 + x) ² 5

2. (-2) ( -½ ) = 1

3. 2(4 ² 5) = (4 ² 5)2

4. x(y ² w) = xy ² xw



Or der of Oper ations

1. Parenthesis/Gr ouping Symbols ² Per for m oper ations within the inner most gr ouping symbolsaccor ding to Steps 2-4 below

2. E xponents/Power s ² Per for moper ations indicated by exponents

3. Multiplication and/or Division ² Per for m multiplication and division inthe or der they occur left to r ight

4. Addition and/or Subtr action ² Per for m addition and subtr action inthe or der they occur left to r ight



Grouping Symbols

Gr ouping symbols include parenthesis, br aces,br ack ets, numer ator s and

denominator s of fr actionsand under neath a r adicalor inside absolute value symbols.



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Number System Power Point