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Section 5.5 Notes Page 1
Ch5.5 Real Numbers & Their Properties
The union of the rational numbers and the irrational numbers is the set of real numbers.
Natural numbers are the number that we use for counting. {1, 2, 3, 4, 5….}
Whole numbers are includes o and the natural numbers. {0, 1, 2, 3, 4….}
Integers includes the whole numbers and the negatives of the natural numbers. {…,-3, -2, -1, 0,
1, 2, 3….}
Rational numbers are the set of all numbers that can be expressed as a quotient of two
integers, with the denominator not 0. Rational numbers can be expressed as terminating or
repeating decimals. {a/b | a and b are integers and b is not 0}
Irrational numbers are the set of all numbers whose decimal representations are neither
terminating nor repeating. Irrational numbers cannot be expressed as a quotient of integers.
𝜋
{√2, −√3, 𝜋, − 2 , … }
Section 5.5 Notes Page 2
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Section 5.5 Notes Page 3
Changing the order in which we subtract and divide real numbers can produce different
answers.
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Ex1. Consider the following set of numbers: {−7, − 4 , 0, 0.6, √5, 𝜋, 7.3, √81}.
List the numbers in the set that are
A. natural numbers. B. whole numbers C. integers. D. rational numbers. E. irrational numbers.
F. real numbers.
𝜋
Ex2. Consider the following set of numbers: {−9, −1.3, 0, 0.3, 2 , √9, √10}.
List the numbers in the set that are
A. natural numbers. B. whole numbers C. integers. D. rational numbers. E. irrational numbers.
F. real numbers.
Ex3. Name the property illustrated:
a) √3 ∙ 7 = 7 ∙ √3
b) (4 + 7) + 6 = 4 + (7 + 6)
d) √2 + (√3 + √7) = √2 + (√7 + √3)
e) 17 + (−17) = 0
c) 2(3 + √5) = 6 + 2√5
f) √2 ∙ 1 = √2