Name _________________________________ Period_________ Date________________
Classifying Real Numbers (page 1)
The set of real numbers consists of all rational and irrational numbers. This relationship can be shown
in a Venn diagram. A rational number is a number that can be written as a quotient of two integers.
The decimal form repeats or terminates. An irrational number is a number that cannot be written as a
quotient of two integers. The decimal form neither terminates nor repeats.
Fill in the Venn diagram with the terms: Real, Rational, Irrational, Integers, Whole, Counting/Natural.
_____ Numbers
________
Numbers
__
_________
_______ Numbers
______ Numbers
π
{0, 1, 2, 3…}
2.1743427…
______________ Numbers
{1, 2, 3…}
A. Classify each real number. Give your reasoning.
Number
10
2
Subset(s)
Natural, Whole, Integer,
Rational
Reasoning
10
5
2
 16
Integer, Rational
 16  4
0.35
Rational
Repeating decimal
14
Irrational

Irrational
3
Irrational
5
14 not a perfect square; decimal does not repeat or
terminate
Decimal form does not repeat or terminate
5 not a perfect cube; decimal does not repeat or
terminate
2
B. Which number is greater, 5 or 2 ? Explain.
3
2  5  3, so 5  2.?
4  
1 1
5   5,  .2
 5
9 
So
5  2.2
And
2
2
 2.6
3
2.6  2.2 so
So
2
2
 5;
3
2
2
is greater.
3
Classifying Real Numbers (page 1)
1. Classify each real number. Give your reasoning.
Number
3
Subset(s)
Reasoning
27
 144

21
2
18
0.123
2. (SBAC) A student claims: “ If a rational number is not an integer, then the square root of the
2
irrational.” Show an
5
example of a rational number that is not an integer to show that this claim in incorrect!
number must be irrational. For example,
2.5 is irrational and so is