Math Analysis/Trigonometry
Palmer High School
Name__________________________
Types of Real Numbers: Natural, Whole, Integer, Rational, and Irrational
Number: A symbol used to communicate value or measurement.
(  ) Real Number:
A number whose value corresponds to exactly one point on the
number line. The set of real numbers includes: Natural, Whole,
Integer, Rational, and Irrational.
(N) Natural or Counting Number: A whole number that belongs to the set 1, 2,3, 4...,  
(W) Whole Number:
A number that is not broken into fractional amounts and that belongs
to the set 0,1, 2,3, 4...,  
(Z) Integer:
A whole number that is either positive or negative that belongs to the
set  ,.....  2, 1,0,1, 2,...,  
(Q) Rational Number:
Any number that can be expressed as a ratio of two integers
(I) Irrational Number:
Any number that cannot be expressed as a ratio or fraction. The
decimal form of an irrational number is non-terminating and
non-repeating. Two examples of an irrational numbers are the
mathematical constant Pi (   3.1415......... ) or 2  1.41421356......... .
m
,
n
where n is not zero. The decimal form of a rational number is either a
1
1
terminating decimal (  0.25 ) or a repeating decimal (  0.16 )
4
6
Name which of the above sets (N, W, Z, Q, I) that each number belongs. A number may belong
to one or more sets:
1.
11
3
7.
20
2.
-12
8.
1.45736972……
3.
0
9.
3
8
4.
7.25
10.
-328.92
5.
4.17
11.
5
6.
36
12.
0.357357357…
Math Analysis/Trigonometry
Palmer High School
Name__________________________
13. Place the following real numbers in numerical order from smallest to largest:
2, 5.2, -3, -0.6,
9
, 0,  3 , 0.4, 0.28
17
14. State whether each statement is true or false.
1
a)
is an integer
f)  is irrational
2
b) -2 is an integer
g) 1.4 is irrational
c) 2 is rational
h) The symbol Q is used for integers
3
d)
is rational
i) Every integer is a rational number
5
e) 7 is a real number
j) 4 is an integer
15. Plot the following numbers on the number line below. Use the associated letter to label
the number’s location. Example: Q) -3.3
 1

 A) , B) 2, C )2.7, D)5, E )  2, F )0.33, G) 5, H )6 
 2

Q
-6 -5 -4 -3 -2 -1 0 1 2
3 4
5 6 7
16. Simplify each expression and determine whether the solution belongs to the set of
integers, rational or irrational numbers.
a) 3  13
2 1
b) 
5 5
e)
c) 8  2 2
g) 16 
d) 5 – 11.2
h)
2  3.5
f) 56  7
1
3
53