SOL 8.2 REAL NUMBER SYSTEM
NATURAL NUMBERS

Natural numbers are the set of counting
numbers.

{1, 2, 3, 4, 5……..}
Natural
WHOLE NUMBERS

Whole numbers are the set of all natural
numbers and zero.

{0, 1, 2, 3, 4, 5.……}
Whole
Natural
INTEGERS

Integers are the set of whole numbers and their
opposites.

{…..-4, -3, -2, -1, 0, 1, 2, 3, 4…..}
Integers
Whole
Natural
RATIONAL NUMBERS

Rational numbers are numbers that can be written as
fractions and do not equal zero. Rational numbers include
terminating and repeating decimals.
 {√36, 0.252525…., 3/8, 4/9, -√225}
Rational
Integers
Whole
Natural
IRRATIONAL NUMBERS

Irrational numbers are the set of all non-repeating, nonterminating decimals. An irrational number cannot be
expressed as an integer.

{ ∏, √2, 1.732050806…., -√7}
Rational
Integers
Whole
Natural
Irrational
REAL NUMBERS

Real numbers are the set of all rational and
irrational numbers.
Real Numbers
Rational
Integers
Whole
Natural
Irrational
WHAT BELONGS WITH WHAT?

If a number belongs to the subset of natural, it
also belongs to the subsets of whole, integer,
rational, and real.
Real Numbers
Rational
Integers
Whole
Natural
*Since natural numbers are
inside all the other circles,
they belong to all of the
subsets.
WHAT BELONGS WITH WHAT?

If a number belongs to the subset of whole, it also
belongs to the subsets of integer, rational, and
real.
Real Numbers
Rational
Integers
Whole
Natural
*Since whole numbers are
inside integers and
rational, they belong to
those subsets as well.
WHAT BELONGS WITH WHAT?

If a number belongs to the subset of integer, it
also belongs to the subset of rational and real.
Real Numbers
Rational
Integers
Whole
Natural
*Since integers are
inside rational, they
belong to that subset as
well.
WHAT BELONGS WITH WHAT?

A number is either rational or irrational. IT
CANNOT BELONG TO BOTH SUBSETS!
Real Numbers
Rational
Integers
Whole
Natural
Irrational
EXAMPLES

Which of the following does not represent a
rational number?
A. 0
 B. 2 ½
 C. √3
1
 D.  10

C. √3
EXAMPLES

The set of whole numbers is not a subset of –
A.
 B.
 C.
 D.

irrational
integers
rational numbers
real numbers
A. irrational
EXAMPLES

Which of the following does not contain the
number 24?
A.
 B.
 C.
 D.

Integers
Whole numbers
Natural numbers
Irrational numbers
D. Irrational numbers
EXAMPLES

Which of the following is not a rational number?
A.
 B.
 C.
 D.

-0.75
0
√4
√15
D. √15
EXAMPLES

Which set of numbers contains √5?
A.
 B.
 C.
 D.

Natural numbers
Irrational numbers
Integers
Rational numbers
B. Irrational numbers
EXAMPLES

Which set contains -√49?
A.
 B.
 C.
 D.

Rational numbers
Natural numbers
Irrational numbers
Whole numbers
A. Rational numbers
EXAMPLES

Which subset of real numbers does not contain
the number 0?
A.
 B.
 C.
 D.

Whole numbers
Rational numbers
Integers
Natural numbers
D. Natural numbers