1.1
Real Numbers and Number Operations
Using Real Number Lines
The numbers used
most often in algebra are real numbers. Some important subsets of the
real numbers are listed below.
|
Whole Numbers |
0, 1, 2, 3, … |
|
Integers |
…, -3, -2, -1, 0, 1, 2, 3, … |
|
Rational Numbers |
Real numbers that can be written
as the ratio of two integers. When written as decimals, rational numbers
terminate or repeat: ¾= 0.75 |
|
Irrational Numbers |
Real numbers that are not
rational, such as the square root of 2 and . When written
as decimals, irrational numbers neither terminate nor repeat. |
Real numbers can
be pictured as points on a line called a real number line. The numbers
increase from left to right, and the point labeled 0 is the origin.
Drawing a point is called graphing or plotting the point.
Example:
Graph 3, 5, 7.
Ordering Real Numbers
Use a number line to order the real numbers. Begin by graphing both numbers.
a. -2 and
3
b. -1 and -3
a. Because -2 is to the left of the
3, it follows that -2 is less than 3, which can be written as -2 <
3. This relationship can also be written as 3 > -2, which is read as
"3 is greater than -2."
b. Because -3 is to the left of -1,
it follows that -3 is less than -1, which can be written as -3 < -1. You can
also write -1 > 3.
Identifying Properties of
Real Numbers
The opposite or additive
inverse of any number a is –a. The reciprocal
or multiplicative inverse of any non zero number a is
1/a. Subtraction is defined as adding the opposite, and division is
defined as multiplying by the reciprocal.