Pre-Algebra Chapter 9

Example 1
Classify Real Numbers
Name all of the sets of numbers to which each real number belongs.
a. 9 This number is a natural number, a whole number, an integer,
and a rational number.
b. 0.3 – This repeating decimal is a rational number because it is
equivalent to 1 3 . 1 3 0.33333…
c. 67 67 8.185352772… It is not the square root of a perfect
square so it is irrational.
d. 2 8
Since 2 8
7, this number is an integer and a rational number.
4
4
e. 121 Since 121 11, this number is an integer and a rational
number.
Classification of Numbers
Example Natural Whole Integer Rational Irrational Real
0
4
7
25
41
3 4
0.121212…
0.010110111…
Example 2
Compare Real Numbers on a Number Line
a. Replace with , , or to make 34 5 3 a true statement.
8
Express each number as a decimal. Then graph the numbers.
34 5.830951895…
5 3 8 5.375
5 3 8 34
5 5.1 5.2 5.3 5.4 5.5 5.6 5.7 5.8 5.9 6
Since 34 is to the right of 5 3 8 , 34 53 8 .
Study Tip
Look Back
To review comparing
fractions and decimals,
see Lesson 5-1.
b. Order 4 1 2 , 17, 4.4– , and 16 from least to greatest.
Express each number as a decimal. Then compare the decimals.
4 1 2 4.5
17 4.123105626…
4.4 – 4.444444444…
16 4
16
17
4.4
4 4.1 4.2 4.3 4.4 4.5 4.6 4.7 4.8 4.9 5
4 1 2
From least to greatest, the order is 16, 17, 4.4, 4 1 2 .
442 Chapter 9 Real Numbers and Right Triangles