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aji
 Real numbers consist of all the rational and
irrational numbers.
 The real number system has many subsets:
 Natural Numbers
 Whole Numbers
 Integers
 Natural numbers are the set of counting
numbers.
{1, 2, 3,…}
 Whole numbers are the set of numbers that
include 0 plus the set of natural numbers.
{0, 1, 2, 3, 4, 5,…}
 Integers are the set of whole numbers and
their opposites.
{…,-3, -2, -1, 0, 1, 2, 3,…}
 Rational numbers are any numbers that can
be expressed in the form of , where a and b
are integers, and b ≠ 0.
 They can always be expressed by using
terminating decimals or repeating decimals.
b
a
 Terminating decimals are decimals that
contain a finite number of digits.
 Examples:
36.8
0.125
4.5
 Repeating decimals are decimals that contain a infinite
number of digits.
 Examples:
 0.333…

 7.689689…
FYI…The line above the decimals indicate that number
repeats.
9.1
 Irrational numbers are any numbers that cannot be
expressed as .
 They are expressed as non-terminating, non-
repeating decimals; decimals that go on forever
without repeating a pattern.
 Examples of irrational numbers:
0.34334333433334…
45.86745893…
 (pi)

b
a
π
2
 …(ellipsis)—continues without end
 { } (set)—a collection of objects or numbers.
Sets are notated by using braces { }.
 Finite—having bounds; limited
 Infinite—having no boundaries or limits
 Venn diagram—a diagram consisting of circles
or squares to show relationships of a set of
data.
Irrational NumbersRational Numbers
 Classify all the following numbers as natural, whole, integer,
rational, or irrational. List all that apply.
a. 117
b. 0
c. -12.64039…
d. -½
e. 6.36
f.
g. -3
π
π
9
4
2
1
−
9
4
Rational Numbers
Integers
Whole Numbers
Natural
Numbers
Irrational Numbers
-12.64039…
117
0
6.36
-3
 Now that all the numbers are placed where they belong in
the Venn diagram, you can classify each number:
 117 is a natural number, a whole number, an integer,
and a rational number.
 is a rational number.
 0 is a whole number, an integer, and a rational number.
 -12.64039… is an irrational number.
-3 is an integer and a rational number.
6.36 is a rational number.
 is an irrational number.
 is a rational number.
π
9
4
2
1
−
 When taking the square root of any number
that is not a perfect square, the resulting
decimal will be non-terminating and non-
repeating. Therefore, those numbers are
always irrational.
Aji

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Aji

  • 2.  Real numbers consist of all the rational and irrational numbers.  The real number system has many subsets:  Natural Numbers  Whole Numbers  Integers
  • 3.  Natural numbers are the set of counting numbers. {1, 2, 3,…}
  • 4.  Whole numbers are the set of numbers that include 0 plus the set of natural numbers. {0, 1, 2, 3, 4, 5,…}
  • 5.  Integers are the set of whole numbers and their opposites. {…,-3, -2, -1, 0, 1, 2, 3,…}
  • 6.  Rational numbers are any numbers that can be expressed in the form of , where a and b are integers, and b ≠ 0.  They can always be expressed by using terminating decimals or repeating decimals. b a
  • 7.  Terminating decimals are decimals that contain a finite number of digits.  Examples: 36.8 0.125 4.5
  • 8.  Repeating decimals are decimals that contain a infinite number of digits.  Examples:  0.333…   7.689689… FYI…The line above the decimals indicate that number repeats. 9.1
  • 9.  Irrational numbers are any numbers that cannot be expressed as .  They are expressed as non-terminating, non- repeating decimals; decimals that go on forever without repeating a pattern.  Examples of irrational numbers: 0.34334333433334… 45.86745893…  (pi)  b a π 2
  • 10.  …(ellipsis)—continues without end  { } (set)—a collection of objects or numbers. Sets are notated by using braces { }.  Finite—having bounds; limited  Infinite—having no boundaries or limits  Venn diagram—a diagram consisting of circles or squares to show relationships of a set of data.
  • 12.  Classify all the following numbers as natural, whole, integer, rational, or irrational. List all that apply. a. 117 b. 0 c. -12.64039… d. -½ e. 6.36 f. g. -3 π
  • 14.  Now that all the numbers are placed where they belong in the Venn diagram, you can classify each number:  117 is a natural number, a whole number, an integer, and a rational number.  is a rational number.  0 is a whole number, an integer, and a rational number.  -12.64039… is an irrational number. -3 is an integer and a rational number. 6.36 is a rational number.  is an irrational number.  is a rational number. π 9 4 2 1 −
  • 15.  When taking the square root of any number that is not a perfect square, the resulting decimal will be non-terminating and non- repeating. Therefore, those numbers are always irrational.