"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:

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*Rational Numbers:*
examples:

*Fraction*

*Decimal *

-1.5

*Natural Number *

8

*Whole Number *

0

*Integer *

-4

*Irrational Number:*
example:

Number Line