Math Connects, Course 3 69 Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc. 3–4 The Real Number System Numbers that are not are called irrational numbers. The set of rational numbers and the set of numbers together make up the set of real numbers. BUILD YOUR VOCABULARY (pages 62–63) EXAMPLES Classify Numbers Name all sets of numbers to which each real number belongs. 0.090909 . . . The decimal ends in a pattern. It is a number because it is equivalent to . √ 25 Since √ 25 = , it is a number, an , and a rational number. - √ 12 Since the decimal does not repeat or , it is an number. Check Your Progress Name all sets of numbers to which each real number belongs. a. 0.1010101010... b. √ 64 c. √ 13 MAIN IDEA • Identify and classify numbers in the real number system. KEY CONCEPT Irrational Number An irrational number is a number that cannot be expressed as a _ b , where a and b are integers and b ≠ 0.
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Math Connects, Course 3 69
Cop
yrig
ht ©
Gle
ncoe
/McG
raw
-Hill
, a d
ivis
ion
of T
he M
cGra
w-H
ill C
ompa
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, Inc
.3–4 The Real Number System
Numbers that are not are called irrational numbers.
The set of rational numbers and the set of
numbers together make up the set of real numbers.
BUILD YOUR VOCABULARY (pages 62–63)
EXAMPLES Classify Numbers
Name all sets of numbers to which each real number belongs.
0.090909 . . .
The decimal ends in a pattern.
It is a number because it is equivalent to .
√ �� 25
Since √ �� 25 = , it is a number, an
, and a rational number.
- √ �� 12
Since the decimal does not repeat or , it is
an number.
Check Your Progress Name all sets of numbers to which each real number belongs.
a. 0.1010101010...
b. √ �� 64
c. √ �� 13
MAIN IDEA
• Identify and classify numbers in the real number system.
KEY CONCEPT
Irrational Number An irrational number is a number that cannot be
expressed as a _ b , where
a and b are integers and b ≠ 0.
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3–4
70 Math Connects, Course 3
Copyright ©
Glencoe/M
cGraw
-Hill, a division of T
he McG
raw-H
ill Com
panies, Inc.EXAMPLES Graph Real Numbers
Estimate √ � 8 and - √ � 2 to the nearest tenth. Then graph √ � 8 and - √ � 2 on a number line.
Use a calculator to determine the approximate decimal values.
√ � 8 ≈
- √ � 2 ≈
Locate these points on a number line.
0123 1 2 3
√ � 8 ≈ and - √ � 2 ≈ .
Check Your Progress Estimate √ � 3 and - √ � 6 to the nearest tenth. Then graph √ � 3 and - √ � 6 on a number line.
EXAMPLES Compare Real Numbers
Replace each � with <, >, or = to make a true sentence.
3 7 _ 8 � √ �� 15
Write each number as a decimal.
3 7 _ 8 = √ �� 15 =
Since is greater than ,
3 7 _ 8 = √ �� 15 .
ORGANIZE ITOn Lesson 3-4 of your Foldable, summarize the properties of the real number system.
Chapter 3 Real Numbers and thePythagorean Theorem
®
REMEMBER IT Always simplify numbers before classifying them.
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3–4
Math Connects, Course 3 71
Cop
yrig
ht ©
Gle
ncoe
/McG
raw
-Hill
, a d
ivis
ion
of T
he M
cGra
w-H
ill C
ompa
nies
, Inc
. 3.
−2 � √��10.4
Write √��10.4 as a decimal.
√ �� 10.4 ≈
Since 3. − 2 is than 3.224903099...,
3. − 2 √ �� 10.4 .
Check Your Progress Replace each � with <, >, or = to make a true sentence.
a. 3 3 _ 8 � √ �� 14 b. 1.
− 5 � √ �� 2.25
EXAMPLE
BASEBALL The time in seconds that it takes an object to fall d feet is 0.25 √ � d . How many seconds would it take for a baseball that is hit 250 feet straight up in the air to fall from its highest point to the ground?
Use a calculator to approximate the time it will take for the baseball to fall to the ground.
0.25 √ � d = 0.25 Replace d with .
≈ 3.95 or about Use a calculator.
It will take about for the baseball to fall to the ground.
Check Your Progress The time in seconds that it takes an object to fall d feet is 0.25 √ � d . How many seconds would it take for a baseball that is hit 450 feet straight up in the air to fall from its highest point to the ground?
HOMEWORKASSIGNMENTPage(s):
Exercises:
WRITE ITExplain why you can determine that - √ � 2 is less than 1.2 without computation.
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