Properties and Real Numbers

Review and Intro to Algebra 2

Properties and Real Numbers
Taken together, the rational and irrational numbers make up the set of real numbers.

The following examples illustrate some characteristics and properties of real numbers.
1. Classify Real Numbers
a. Whole numbers: a subset of the real numbers; A whole number is either 0 or one of
the “counting numbers,” 1, 2, 3, . . .
b. Integers: A subset of the real numbers; The integers are the set of whole numbers and
their opposites, . . . 23, 22, 21, 0, 1, 2, 3, . . .
c. Rational numbers: A subset of the real numbers; A rational number can be expressed
as the ratio of two integers, and its decimal form terminates or repeats.
d. Irrational numbers: A subset of the real numbers; An irrational number cannot be
expressed as the ratio of two integers, and its decimal form neither terminates nor repeats.


2. Order of Operations: Established rule for evaluating an expression involving more
than one operation:
Step 1: Evaluate expressions inside grouping symbols.
Step 2: Evaluate powers.
Step 3: Multiply and divide from left to right.
Step 4: Add and subtract from left to right.