Pre-Algebra Chapter 9

The Real Number System
Vocabulary
• irrational numbers
• real numbers
• Identify and compare numbers in the real number system.
• Solve equations by finding square roots.
can squares have lengths that are not rational numbers?
In this activity, you will find the length of a side of a square that has an area
of 2 square units.
a. The small square at the right has an area of 1 square
unit. Find the area of the shaded triangle.
b. Suppose eight triangles are arranged as shown. What
shape is formed by the shaded triangles?
c. Find the total area of the four shaded triangles.
d. What number represents the length of the side of
the shaded square?
IDENTIFY AND COMPARE REAL NUMBERS In Lesson 5-2, you
learned that rational numbers can be written as fractions. A few examples of
rational numbers are listed below.
6 8 2 0.05 2.6 5.3 8.12121212… 16
5
Not all numbers are rational numbers. A few examples of numbers that are
not rational are shown below. These numbers are not repeating or terminating
decimals. They are called irrational numbers.
0.101001000100001… 2 1.414213562… 3.14159…
Irrational Number
An irrational number is a number that cannot be expressed as b
a , where a and b
are integers and b does not equal 0.
Concept Check
True or False? All square roots are irrational numbers.
The set of rational
numbers and the set
of irrational numbers
together make up the
set of real numbers.
The Venn diagram at
the right shows the
relationship among
the real numbers.
1
3
Integers
4
0.2
0
Whole
Numbers
2
Real Numbers
Rational Numbers
5
8
3
0.6
Irrational
Numbers
0.010010001...
0.25
2 3 2
Natural Numbers
Lesson 9-2 The Real Number System 441