Download 1 - Ms. Patyi

Algebra 1 Honors
Unit 1.4 Classifying Real Numbers
NOTES
REAL NUMBERS
Rational
NUMBERS
Irrational
NUMBERS
REAL NUMBERS
Identify the category of Real Numbers each number best fits into.
1. 6
6.
2. -4
25
10. { 2 ,  , 5.196…}
3. 0
7.

3
4
11. {-10,
4. 7.5
8. {1,2,3,4,…}
3 , 3.3 , 7.745…, 25}
Reference Glencoe Texbook: Page P7 Chapter 0-2
5.
9. {-8, 3,
7
16
, 9.1}
5
FINITE SET:
Ex: {1, 2, 3, 4}
Ex: {Natural Numbers less than 8}
Ex: {Whole Numbers between 6 and 20}
INFINITE SET:
Ex: {…, 4, 5, 6,…}
Ex: {3, 4, 5…}
Ex: {Integers}
Ex: {Whole numbers greater than 6}
Determine if the number set is Finite or Infinite.
13.
{The number of days in a year}
F
15.
I
{Rational Numbers}
F
14.
I
Reference Glencoe Texbook: Page P7 Chapter 0-2
{…-8, -6, -4, -2, 0}
F
16.
I
{Natural Numbers less than 10}
F
I
Algebra 1 Honors
Unit 1.4 Classifying Real Numbers
ASSIGNMENT
1.
Fill in the table with set of numbers and words below that BEST describe each
number group. (Not in random answer key!)
Fractions
{0, 1, 2, 3, …}
Repeating
Decimals
{…, -1, 0, 1, …}
Rational and
Irrational
Non-perfect Squares
REAL
2.
IRRATIONAL
RATIONAL
{1, 2, 3, …}
INTEGERS
Pi(  )
Terminating
Decimals
Non-terminating
Decimals
WHOLE
NATURAL
Complete the chart. Put an “x” for each set to which the number belongs. You may
be more than one “x” per problem.
Problem
Rational
Integer
Whole
Natural
Irrational
3
a
8
b
5
c
-9
d
0
e

f
-1.5
g
h
1
2
0.67
i
24
j
-100
4
Reference Glencoe Texbook: Page P7 Chapter 0-2
True or False. If the statement is false, give a reason why.
3.
All whole numbers are integers. ______
____________________________
4.
All integers are rational. ______
5.
All decimals are irrational. ______
6.
All rational numbers are real. ______
________________________________
7.
All square roots are irrational. ______
_______________________________
___________________________________
___________________________________
B and C Level
Circle the letter that correctly describes each real number or number set given.
8.
Negative five belongs to which number 9.
Eight belongs to which number
set(s)
set(s)
I. Whole
II. Integer
III. Real
a.
b.
c.
d.
10.
I only
I and II only
III only
II and III only
Zero belongs to which number set(s)
I. Natural
II. Whole
III. Integers
a.
b.
c.
d.
II only
I and II only
II and III only
I, II, and III
Reference Glencoe Texbook: Page P7 Chapter 0-2
I. Natural
II. Whole
III. Integer
a.
b.
c.
d.
I only
I and II only
II and III only
I, II, and III
11.
What set of numbers is
represented by {…-4, -2, 0, 2, 4,...}
a.
b.
c.
d.
Integers
Whole
Natural
Irrational
12.
What set of numbers is represented
by {  , 7 , 0.33 }
a.
b.
c.
d.
13.
What set of numbers is
1
represented by {-4,  , 0, 7, 8.5}
2
Rational
Irrational
Integer
Real
a. Integers
b. Whole
c. Rational
d. Irrational
In questions 14-17, Classify the following sets as:
14.
1

 ,3,2.5,8
2

a.
b.
c.
d.
16.
15.
a.
b.
c.
d.
I
II
III
V
{0, 1, 2, 3, 4}
a.
b.
c.
d.
17.
III
II, III, IV
II, III, IV, V
All
A Level
18. Describe the difference
between a rational and
irrational number.
I.
II.
III.
IV.
V.
{3,
Irrational Numbers
Rational Numbers
Integers
Whole Numbers
Natural Numbers
5, 7, 9, 11}
III, IV, V
II, III, IV
II, III, V
All but I
{-9, -6, -3, 0, 3, 6, 9}
a. III
b. II, III
c. II, III, IV, V
d. All
19. Describe the difference
between an integer and
whole number
Reference Glencoe Texbook: Page P7 Chapter 0-2
20. Describe the difference
between a natural number
and a whole number.
C Level
In 21 – 32, Determine whether the following sets are finite or infinite.
Finite: A set of numbers with both a beginning and end!
Infinite: A set of numbers with no beginning and/or no end.
21.
{natural numbers}
22.
{Whole numbers}
23.
{number of days in a week}
24.
{Negative integers greater than -5}
25.
{-5, -4, -3, -2}
26.
{1, 2, 3, …, 14, 15, 16}
27.
{Real Numbers}
28.
{whole numbers between 0 and 9}
29.
{…-2, -1, 0, 1, 2, …}
30.
{Integers less than 5}
31.
{natural numbers less than 27}
32.
{Integers between –124 and 316}
Directions: Create 3 examples for each type of number set below. B Level
33. Finite
34. Infinite
Example 1: ______________________
Example 1: ______________________
Example 2: ______________________
Example 2: ______________________
Example 3: ______________________
Example 3: ______________________
A Level
35. Explain the difference between a finite and infinite set of numbers. Give an example
for each type in your explanation.
Reference Glencoe Texbook: Page P7 Chapter 0-2
Practice Assessments:
1.4 Assessment (Part 1)
Level C
1C.
–4 best fits into which
category of Real
Numbers?
Level B
Which of the following
categories of Real Numbers
does the number -2 fall into.
1B.
a. Natural
c. Irrational
d. Rational
a.
b.
c.
d.
e.
1.4 Assessment (Part 2)
Level C
Is the following set of
whole numbers finite or
infinite?
Describe the difference
between a Rational and
Irrational Number.
1A.
Circle every possible
answer.
b. Integer
2C.
Level A
Rational
Irrational
Integer
Natural
Whole
Level B
2B.
Create an example of a
finite set.
{…-2, -1, 0, 1,2…}
Reference Glencoe Texbook: Page P7 Chapter 0-2
Level A
Describe the difference
between a finite and infinite
set of numbers. Give an
example of each type of set.
2A.
ANSWERS:
1.
Fill in the table with set of numbers and words below that BEST describe each
number group. (Not in random answer key!)
Fractions
{0, 1, 2, 3, …}
Repeating
Decimals
{…, -1, 0, 1, …}
Rational and
Irrational
Non-perfect Squares
REAL
Rational
And
Irrational
IRRATIONAL



2.
Pi
Non-Term.
Dec.
Non-Perfect
Squares
RATIONAL



{1, 2, 3, …}
INTEGERS
Fractions
Repeating
Dec
Term Dec
{…-1,0,1}
Pi(  )
Terminating
Decimals
Non-terminating
Decimals
WHOLE
{0,1,2,3…}
NATURAL
{1,2,3,…}
Complete the chart. Put an “x” for each set to which the number belongs. You may
be more than one “x” per problem.
Problem
Rational
Integer
Whole
Natural
Irrational
3
a
x
8
b
x
5
c
-9
x
x
d
0
x
x
x
e
x

f
-1.5
x
1
g
x
4
2
h
x
0.67
i
24
x
x
x
x
j
-100
x
x
True or False. If the statement is false, give a reason why.
3.
All whole numbers are integers. __True__ ____________________________
4.
All integers are rational. _True_
___________________________________
5.
All decimals are irrational. __False_
6.
All rational numbers are real. _True_
7.
All square roots are irrational. _False_
Reference Glencoe Texbook: Page P7 Chapter 0-2
Repeating and Term. Decimals are Rational
________________________________
Perfect Squares are rational
Answers cont…
8. d
9. d
14. b
15. d
20. will vary
21. Inf
26. Fin
27. Inf
32. Fin
33. See
examples in
problems 2133.
10. c
16. b
22. Inf
28. Fin
34. See
examples in
problems 2133.
11. a
17. b
23. Fin
29. Inf
35. Fin-Sets
terminate
Infinite-Sets
do not
terminate
12. d
18. will vary
24. Fin
30. Inf
13. c
19. will vary
25. Fin
31. Inf
Practice Assessments
1C b
1B a,c
1A
2C Infinite
2B
2A
Rational
numbers include all
integers, fractions
and terminating and
repeating decimals.
Irrational numbers
only include nonterminating, nonrepeating decimals.
Reference Glencoe Texbook: Page P7 Chapter 0-2
Answers
Vary
{1,2,3,4}
Finite is a set
of numbers that
terminates (ends)
{1,2,3,4}
Infinite is a set of
numbers that does
not terminate.
{…1,2,3,4…}