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Name: ___________________________________________ Period: __________ Date: ________________
THE COMPLEX NUMBER SYSTEM
Natural Numbers – (N) - The set of numbers that you count with. N = {1, 2, 3, …}
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Whole Numbers – (W) – The set of Natural Numbers and zero. W= {0, 1, 2, 3, …}
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Integers – (J) - The set of Integers and their opposites. J = {…-3, -2, -1, 0, 1, 2, 3, …}
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Opposites – Two number that are exactly the same distance from zero on the number line.
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Rational Numbers – (Q) – Any number that can be expressed as a ratio of two integers, a and b, where b 
0.
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Terminating Decimal – A decimal number with a finite number of nonzero digits after the decimal point. It
ends.
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Repeating Decimal – A decimal number with a digit or group of digits after the decimal point that repeats
indefinitely
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Irrational Numbers – Any number that cannot be expressed as a ratio of two integers, a and b, where b  0.
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Real Numbers – Any number that has a place on the number line.
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Imaginary Numbers – Any number that does not have a place on the number line.
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 Label the Venn diagram below to show the relationships between the subsets of the
Complex Number System. Use symbols when possible.
The Complex Number System

Imaginary
Q
J
Irrational
W
N
 Examples: All boxes that describe the given number are marked.
REAL
NOT REAL
Number
Natural
Whole
Integer
Rational
7







0

2
2
3
2
Imaginary

2.37
3
Irrational




 Mark each box that describes the given number. Select all that apply.
Number
Natural
Whole
Integer
Rational






1)
25
2)
 14
3)
5
7

4)
0.32

5)
 3.76

6)
8
7)
100
8)
0.47892…
9)
9.39
10)
9
11)

Irrational
Imaginary









 List two examples of a fraction whose decimal form terminates.
 List two examples of a fraction whose decimal form repeats.
 What is the opposite of 5?– 5
 What is the opposite of  ? –
1
3
;
1
2
;
1
4
1
6
; and others
; and others
 Write each number on the line below each subset of the set of Real Numbers so that each
subset has at least one example.
6
16
0
0.27
0.27
0.33 13
4
 9

2
9
2
3
2
5
25
REAL NUMBERS
Rational
Numbers
Irrational
Numbers
Integers
Opposites of
Natural Numbers
Fractions
Terminating
Decimals
Whole
Numbers
Natural
Numbers
Zero
0.27
0
Odd
Numbers
3
Even
Numbers
16

Repeating
Decimals