Skills Workshop
Rational and Irrational Numbers
All real numbers are classified as rational or irrational numbers.
A rational number is any number that can be written as a decimal that terminates or repeats. A
repeating decimal is one that has a repeating pattern of digits to the right of the decimal point. An
irrational number is any number that cannot be written as a decimal that terminates or repeats. A
commonly used irrational number is π. The list below summarizes types of numbers that are rational
numbers and irrational numbers.
Rational Numbers
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•
•
•
•
Irrational Numbers
whole numbers
decimals that terminate
decimals that repeat
negative integers
fractions that have an integer in the numerator and
in the denominator
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•
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fractions that cannot be written with integers in
the numerator and the denominator
decimals that do not terminate
decimals that do not repeat
radical expressions that do not have a perfect
square under the radical sign
EXAMPLE 1
Identify the number 78 as rational or irrational.
SOLUTION
The number 78 is a whole number, so 78 is a rational number.
EXAMPLE 2
Identify the number 2.25 as rational or irrational.
SOLUTION
The number 2.25 is a decimal that terminates, so 2.25 is a rational number.
EXAMPLE 3
Identify the number 14 as rational or irrational.
SOLUTION
The number 14 is not a perfect square, so 14 is an irrational number.
EXAMPLE 4
SOLUTION
Identify the number 81 as rational or irrational.
The number 81 is a perfect square, so 81 is a rational number.
EXAMPLE 5
Identify the number
SOLUTION
The numbers in the numerator and denominator are integers, so
2
as rational or irrational.
5
2
is a rational number.
5
Identify each number as rational or irrational.
1. 8.1
2. 18
6. 12
7.
1
3
3. 0.675
4.
8.
9. 10
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5. 9.3481…
10.
5
16