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Positive and Negative Integers
Positive integers are all the whole numbers greater than zero: 1, 2, 3, 4, 5, ... . Negative integers
are all the opposites of these whole numbers: -1, -2, -3, -4, -5, … .
Zero is not considered to be a
positive or negative number. For each positive integer, there exists a negative integer are called
opposites. For example, -9 is the opposite of
9, -21 is the opposite of 21, and 18
is the opposite of
-18. If an integer is greater than zero, we say that its sign is positive. If an integer is less than zero,
we say that its sign is negative.
The Number Line
The number line is a line labeled with the integers in increasing order from left to right, that
extends in both directions:
Absolute Value of an Integer
The absolute value of a number is always a positive number (or zero). We specify the absolute
value of a number n by writing n in between two vertical bars: |n|.
Examples:
|16| = 16
|-12| = 12
Real Numbers: Any number that can name a position on a number line is a real number.
Every position on a number line can be named by a real number in some form.
An important property of real numbers is the Density Property. It says that between any two real
numbers, there is always another real number.
Rational Numbers: Any number that can be written in fraction form is a rational number. This
includes integers, terminating decimals, and repeating decimals as well as fractions.
Angles can
be classified by their measures, as seen in the following figure.
• An integer can be written as a fraction simply by giving it a denominator of one, so any integer
is a rational number.
• A terminating decimal can be written as a fraction simply by writing it the way you say it: 3.75 =
three and seventy-five hundredths =
 , then adding if needed to produce a
fraction:
 . So, any terminating decimal is a rational number.
• A repeating decimal can be written as a fraction using algebraic methods, so any repeating
decimal is a rational number.
Whole Numbers: Zero and the positive integers are the whole numbers.
Natural Numbers: Also called the counting numbers, this set includes all of the whole numbers
except zero (1, 2, 3, ....)
Irrational Numbers: Any real number that cannot be written in fraction
form is an irrational number.
These numbers include the non-terminating, non-repeating decimals (pi,
0.45445544455544445555..., 2, etc.). Any square root that is not a perfect root is an irrational
number. For example, 1 and 4 are rational because 1 = 1 and
4 = 2, but 2 and 3 are irrational-
there are no perfect squares between 1 and 4. All four of these numbers do name points on the
number line, but they cannot be written as fractions. When a decimal or fractional approximation for
an irrational number is used to compute (as in finding the area of a circle), the answer is always
approximate and should clearly indicate this.
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