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Practice D

Unit 1

Real Numbers

Getting

Ready

Most likely, all the numbers you’ve encountered in math classes so far have

been real numbers. Real numbers are the ones you use in real life, from a career

in accounting to reading the date off a calendar. So, it’s important that you

get to know their characteristics. The following chart shows some important

sets of numbers that are subsets of the real numbers.

Subsets of Real Numbers

Natural Numbers

The numbers you use to count.

1, 2, 3, 4, . . .

Whole Numbers

The natural numbers and 0.

0, 1, 2, 3, 4, . . .

Integers

The natural numbers, their opposites, and 0.

. . . , −4, −3, −2, −1, 0, 1, 2, 3, 4, . . .

Rational Numbers

Numbers that can be written as quotients of integers. In decimal

form, they can be written as terminating or repeating decimals.

__

Ex. 1

67 , −2 8

__

__

, 0.07, 5.

, 4

2

9

Irrational Numbers

Numbers that cannot be written as quotients of integers. In

decimal form, they do not terminate or repeat.

__

___

3

Ex.

2 , π,

70

√

√

The diagram below can help you understand how the subsets of real numbers

are related. As you can see, all real numbers are either rational or irrational, and

the natural numbers are the smallest category in the diagram.

Real Numbers

Rational Numbers

Integers

Whole Numbers

Irrational Numbers

Natural Numbers

EXAMPLE 1

Classify each of the following numbers as rational or irrational:

____

9.

1234 , 0.73625…, 0

If the number is rational, list all other classifications that apply.

____

Rational numbers include repeating and terminating decimals, so 9.

1234 is

rational. 0.73625… is neither repeating nor terminating, so it is irrational. 0 is

rational and it is also included in the set of integers and whole numbers.

____

Solution: 9.

1234 is rational. 0.73625… is irrational. 0 is rational, as well as an

integer and a whole number.

D-1

Algebra 2, Unit 1 • Linear Systems and Matrices

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