2. Math Objective
The student will be able to:
Describe and classify Types of Numbers in the
Real Number System
3. Real Numbers
The Real Number System consists of both
Rational and Irrational Numbers. These
numbers can be pictured as points on a
Real Number Line:
4. Rational Numbers
Natural Numbers – set of counting numbers
{1, 2, 3, 4, 5, 6, ...}
Whole Numbers – set of natural numbers
that include the number ‘0”
{0, 1, 2, 3, 4, 5, 6, …}
Integers – set of whole numbers and their
opposites
{…,-3, -2, -1, 0, 1, 2, 3, …}
5. Definition
Rational Numbers are any numbers that can be
expressed in the form of a/b, where a and b are
integers and b ≠ 0.
For example, integers can be written with a
denominator of 1
{…, -3/1, -2/1, -1/1, 0/1, 1/1, 2/1, 3/1, …}
Rational numbers can also be expressed by using
terminating decimals or repeating decimals.
6. Terminating decimals are decimals that
contain a finite number of digits.
For example:
0.75, 2.5, -10.25, -0.5, …
Note: The example terminating decimals
respond to the fractions 3/4, 2½, -10¼, -½
Repeating decimals are decimals that contain
an infinite number of digits.
For example:
0.333…, -2.666…, 0.8181
Note: The example repeating decimals
respond to the fractions 1/3, -2 2/3, 9/11
7. Irrational Numbers
An Irrational Number is a number that cannot be
written as a fraction and the decimal equivalent
does not terminate nor repeat.
For example:
Π (Pi) is an irrational number. The value of Π is:
3.1415926535897932384626433832795…
Radical numbers that cannot simplify to a
rational number are irrational:
√2 ≈ 1.414213562373095…
³√7 ≈ 1.912931182772389…
8. The Real Number System Summary
Real Numbers
http://nowiunderstandmath.com/nium_distance_edu_course.html
