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Real Numbers
The set of real numbers consists of the set of rational numbers and the
set of irrational numbers.
REAL NUMBERS
Rational #s
Irrational #s
a
A Rational number is any number that can be written as a ratio,
where a and b are integers and b ≠ 0.
REAL NUMBERS
Rational #s
b
Irrational #s
Integers
Whole Numbers
Integers are whole numbers and their opposites.
Examples: 1, 6, 9, 87, 126
REAL NUMBERS
Rational #s
Irrational #s
Integers
Whole Numbers
Terminating and
Repeating decimals
Decimals that terminate are rational numbers.
Examples: 1.2, 6.378, 8.92, 12.6
Decimals that repeat are rational numbers.
Examples: 1.2, 6.378, 8.92, 12.6
An Irrational number can only be written as decimals that do NOT terminate or repeat.
REAL NUMBERS
Rational #s
Irrational #s
Integers
Whole Numbers
Non-terminating &
Terminating and
Non-repeating
Repeating decimals
decimals
Classifying Numbers Notes, Page 1
If a whole number is not a perfect square, then its square root is an Irrational number.
Example: √2 = 1.41421356237309…
Example: √10 = 3.162277660…
REAL NUMBERS
Rational #s
Irrational #s
Integers
√2
∏
Whole Numbers
Non-terminating &
Terminating and
Non-repeating
Repeating decimals
decimals
∏, pi, is an irrational number because it does not terminate or repeat.
The set of real numbers consist s of the set of rational numbers and the
set of irrational numbers.
REAL NUMBERS
Rational #s
Integers
Irrational #s
√2
∏
Whole Numbers
Non-terminating &
Terminating and
Non-repeating
Repeating decimals
decimals
Real numbers include the set of rational and irrational numbers.
There are numbers that are classified as NOT REAL
These numbers are not rational OR irrational!
Ex 1:
Ratios with zero as the denominator
6
0
Ex 2:
Negative values under the radical symbol
√-5
You need to be able to classify all numbers.
Write all names that apply to each number:
√2
Ex 1:
Real Number; Irrational
Ex 2:
-56.85
Real Number; Rational
Ex 3:
√9
Real Number; Whole, Integer, Rational
3
Classifying Numbers Notes, Page 2
Determine the Classification of all numbers
State if the number is Rational, Irrational, or not a Real number:
√8
Ex 1:
Irrational number
Ex 2:
11
Rational number
Ex 3:
3
0
Not a Real number
Ex 4:
-258
Rational number
Ex 5:
√¼
Rational number
Ex 6:
√-17
Not a Real number
Ex 7:
34.5
Rational number
Classifying Numbers Notes, Page 3
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