  ## Real Numbers . . . The practical numbers of everyday life . . . "Numbers"   Real Numbers include all numbers whose decimal form can be represented graphically, as a point located on a number line. Number Line

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

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

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: "Top of Page"

Rational Numbers: examples:

Fraction Decimal

-1.5

Natural Number

8

Whole Number

0

Integer

-4

Irrational Number: example:  Number Line