Beginning Algebra, 11th Edition

Not all numbers are rational. For example, the square root of 2, written , cannot

be written as a quotient of two integers. Because of this, is an irrational number.

(See FIGURE 6.)

 2

 2

30 CHAPTER 1 The Real Number System

1

1

11 √^2

This square has diagonal

of length √2. The number

√2 is an irrational number.

FIGURE 6

Irrational Numbers

is a nonrational number represented by a point on the number line is the

set of irrational numbers.

5 x|x 6

The decimal form of an irrational number neither terminates nor repeats.

Both rational and irrational numbers can be represented by points on the number

line and together form the set of real numbers.

Real Numbers

5 x|xis a rational or an irrational number is the set of 6 real numbers.*

*An example of a number that is not a real number is the square root of a negative number, such as

†The value of (pi) is approximately 3.141592654. The decimal digits continue forever with no repeated pattern.p

- 5.

The relationships among the various sets of numbers are shown in FIGURE 7.

Rational numbers

Real numbers

Irrational numbers

Integers

..., –3, –2, – 1

Whole

numbers

Natural

numbers

0

1, 2, 3,...

• 8
  15
  23

4

π†

π

4

-^1
5
–3^2

• 0.125 1.5 0.18

9

4

7

11

FIGURE 7

Determining Whether a Number Belongs to a Set

List the numbers in the following set that belong to each set of numbers.

(a)Natural numbers: 5

(b)Whole numbers: 0 and 5

The whole numbers consist of the natural (counting) numbers and 0.

e-5, -

2

3

, 0, 0.6,  2 , 3

1

4

, 5, 5.8f

EXAMPLE 2

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