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Real Numbers
. . .
The practical numbers of
everyday life . . .









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Real Numbers - Heading


Real Numbers include all numbers whose decimal form can be represented graphically, as a point located on a number line.


Number Line

Number Line


"Real" Numbers do not include imaginary or complex numbers.



Only the following types of numbers are "real" numbers:

ZZZZZ

Rational Numbers: Rational numbers are numbers which can be represented by a ratio (a fraction).


Fractions

All Fractions . . .


Decimals - two separate types of decimals are rational numbers

only terminating and repeating decimals . . .

(Non-terminating, non-repeating decimals such as π (≈ 3.14159...), Euler's mathematical constant e (≈ 2.71828...), or √2 (≈ 1.4142...) are not rational numbers. They are called irrational numbers.)


Natural Numbers - (counting numbers)

1, 2, 3, 4, 5, . . .


Whole Numbers - (counting numbers plus zero)

0, 1, 2, 3, 4, 5, . . .


Integers - (whole numbers plus negative whole numbers)

. . . -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, . . .



Irrational Numbers: Irrational numbers are numbers whose decimal equivalent is non-terminating and does not have a repeating pattern.



The following examples of "real" numbers are shown on the number line , below:


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Rational Numbers: examples:


Fraction

Fraction - one-half

Decimal

-1.5


Natural Number

8


Whole Number

0


Integer

-4



Irrational Number: example:


Irrational Number - Pi



Number Line - showing examples

Number Line