Name
Date
All Problems On This Page
Practice A
LESSON
1-1
Class
Sets of Numbers
Order the given numbers from least to greatest.
_
3
1. 2.6, 27 , __
, 1.8
4
a. Rewrite each number as a decimal.
5.29
2 7 _ 0.75
2.6, 0.75, 1.8, 5.29
_
3
3
__
4
b. Order the decimals.
2.6, __, 1.8, 2 7
4
c. Order the original numbers.
Order the given numbers from least to greatest.
1
6
3. 2 , __
, 5.916, ___
8
11
2 __
2. 2.8, 10 , __
,9
11 7
9, 2.8, 2 , __
___
10
6, __
1
5.916, 2 , ___
11 8
11 7
_
, 3.14
7 , 4. ___
23 , ___
5
4
1 , 6.159, , 6.5
5. 6__
8
_
7 , ____
, 3.14, ____
23
5
1, , 6.159
6.5, 6__
8
4
Classify each number. Write all classifications that apply:
real, rational, integer, whole, natural.
_
6. 4.357
Real, rational
7
7. __
4
Real, rational
Real, rational, integer
8. 6
Rewrite each set using the notation indicated.
{ x |6 x 4 }
9. (6, 4]; set-builder notation
All real numbers between 4 and 6
10. 4 x 6; words
including 4 but not including 6
[10, )
11. { x |x 10 }; interval notation
12.
{ 5, 3, 1, 1, 3, 5 }
roster notation
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Holt Algebra 2
12/20/05 1:24:15 PM
Process Black
Name
Date
LESSON
1-1
Class
All Problems On This Page
Practice B
Sets of Numbers
Order the given numbers from least to greatest. Then classify each
number by the subsets of the real numbers to which it belongs.
_
1 , ⫺4.9
2 , 6.17, 兹
28 , ⫺3__
1. __
3
8
_
⫺8
, 4.615, 0
2. 5␲, ⫺6兹3 , ___
3
Rewrite each set in the indicated notation.
3. negative multiples of 3; set-builder notation
4. [⫺4, 0) or (10, 21); words
5.
6.
roster notation
set-builder notation
The length of a necktie is generally in the range 52, 58 inches. The
width of a tie is in the range 2.75, 3.5 inches. Use this information
for Exercises 7–8.
7. Represent the range of the length of neckties in
roster notation. Assume that all neckties come
in whole-inch lengths.
8. Represent the range of the width of neckties
in set-builder notation.
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All rights reserved.
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Holt Algebra 2
3/23/06 8:24:34 AM
Name
LESSON
1-1
Date
Class
All Problems On This Page
Practice C
Sets of Numbers
Use the table for Exercises 1–5.
1. Order the densities of the minerals from least
to greatest.
Density of Some Minerals
1 , 2.16, 3___
7 , 3.86, 4__
2
1.68, 2____
5
100
40
Mineral
2. Which subset of real numbers best describes
the densities of these minerals?
Aluminite
3. Explain why the densities cannot be represented
using set-builder notation.
Possible answer: There is no pattern to
the numbers so they cannot be described
Fluorannite
Graphite
2.16
Titanium
2
4__
5
Ziesite
in set-builder notation.
1.68
1
2____
100
7
3___
40
Cryptohalite
Rational numbers
3
Density (g/cm )
3.86
4. Use interval notation to describe a set of numbers
that contains the densities of the minerals.
Possible answer: 1, 5 5. What types of real numbers are NOT shown in the table?
Irrational numbers, integers, whole numbers, and natural numbers
Tell whether each statement is true or false. If false, give a
counterexample.
6. All real numbers are rational numbers.
False; possible answer: 7. Every member of the interval (0, 8] is a natural number.
False; possible answer: 3.3
Solve.
8. Use interval notation to express the set of numbers NOT represented
on the number line.
(, 5), [2, 1], and [4,)
9. Identify one rational number and one irrational number that are members of the
interval 8, 8 .
Possible answer: 7 and 2
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Holt Algebra 2
12/20/05 1:24:17 PM
Process Black
Name
Date
LESSON
1-1
Class
All Problems On This Page
Problem Solving
Sets of Numbers
Ari is comparing the density of some common substances. Density
measures how compact a substance is. Use the data in the table for
Exercises 1–3.
1. Ari begins by ordering the densities from least
to greatest. Write his ordered list.
Substance
Air
2. Should Ari use roster, interval, or set-builder
notation to represent his data? Why?
3. Which subset of the real numbers best
describes the densities given in the table?
Choose from , , , and .
Copper
Density kg/m 3
3
1___
10
Helium
8.9
9
___
50
Hydrogen
0.09
Milk
1030
Olive oil
900
Choose the letter for the best answer.
4. Jean wrote the possible readings on
the speedometer of her new car in setbuilder notation. Which could be what
she wrote?
A { x | 0 ⬎ x ⬎ 120 }
B { x | x ⫽ 10n and n ⱕ 12 }
C { 10, 20, 30, 40, 50, ), 120 }
D { x | 0 ⱕ x ⱕ 120 }
5. Members of the Booster Club are
designing a calendar of the school year
to sell as a fund raiser. They begin by
making a roster of the possible number
of days in a month. Which shows the
roster?
F { 30, 31 }
G { x | 28 ⱕ x ⱕ 31 }
H { 28, 29, 30, 31 }
J { x | x ⱖ 28 and x 僆 }
Tell whether each statement is true or false. If false, give a
counterexample.
7. Neil and Sandy are cutting out circles
as decorations. Sandy comments that
the distance around a circle is always a
rational number.
6. Trish and Alex are comparing the
populations of different cities in Texas.
Alex says the population of a city is
always an integer.
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Holt Algebra 2
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