Download File - Ms. Pendergast`s Math Class

Notes: Classify Numbers
To classify numbers means to put numbers into ___________________________.
What other things do you put into categories, or _________________?

____________________________________
Real Numbers
________ number that I ________ now.
Real numbers are split into ______ big categories: ___________ and ____________ numbers.
Rational Numbers
Ratio means __________
Examples:
0
5
-12
1
Irrational Numbers
The prefix “IR-” means _______, so IRrational means _____ ________
Decimals have….
No _____ AND No _______ __________
-567,023,234.456
36  is a perfect square, = 6
Examples:
2  not a perfect square, =1.4142136… 
no end and no repeating pattern
  no end and no repeating pattern
234.2315891  has an end
54.234234234234… has a repeating pattern
-9.5623 decimals have an end
0.24244244424444…  no end and no
repeating pattern
-0.33333…..  decimals have a pattern
Label these numbers as rational (R) or irrational (IR)
0.999 0.24
0
4
3.99813
2
3.99813…
246
1000
 ( pi)
¾

-5
6.3
A
3.1415…
2
4
4
3.9898989…
3
0.33333…
99/100
3
6
4
-3.98988988898888…
(-990)
3
-4.5
9
25
7
7 11 81 121 144 100 14 36 45 49
B½ ¾
¼
 1512 234
653
12 23
234
15
 653
12 23 12  12
15 23653
234
12
 15  653234
234
 65378
15  653
78
23  15
78
23 78
7823 234 78
65
65
987
987
65
987
65
987
65 9871414 987987
124 124 987
1665
16987 14
124
987
 1698714
124
987 14  16  16
124 14
124
 16
C -4 -16 -125
-5
0
-9,123
-6 ¾
-500
-1,000,000
D -34.4567437 -23.23232… -1,123.12351512… -15.09874…
-2.344344…
E0
0
F 5.3
G -14
1
4
-19.4
16
22/7
0.12345
1,098,836
π
-24
0.125
0.234234234…
2
5
2/5
2.51551555…. 14
0.1987652346…
-4 ½
4.2
8.123413254 6.5
0.344344434344…
More types of RATIONAL numbers
Rational numbers are split into __________ smaller categories: ____________, ___________, & _____________

A natural number is ______________________________________________________
o Examples: ________________________ Is NOT: _________________________
Ways to remember:

A whole number is _______________________________________________________
o Examples: ________________________ Is NOT: _________________________
Ways to remember:

An integer is ____________________________________________________________
o Examples: ________________________ Is NOT: _________________________
Ways to remember:
Label these numbers as
 Integers (lower-case i)
 Natural numbers (n)
 Whole numbers (w)
*** remember, a number can be more than one type ***
0
6
-56
1
-1245
1,500,789
3.0
7
16
-76
-1,500,789
56
-900
-15
1.654
4
4
-3.0
-676
4
4
24
3
 27
9
Multiple Choice: Explain why you chose/ eliminated answers
1. Which student provided the most accurate definition of the set of all natural numbers?
A.
B.
C.
D.
Angela: “The set of all natural numbers is all real numbers except fractions.”
Ben: “The set of all natural numbers is all positive numbers but not 0.”
Carlene: “The set of all natural numbers is all whole numbers and their negatives.”
Diego: “The set of all natural numbers is decimals, fractions, and negatives.”
2. Which name best describes the set of numbers to the right?
A.
integers
B. whole numbers C. natural numbers
{0, 0.5, 1, 2, 4}
D. rational numbers
3. Which set below is the set of all whole numbers?
A.
{1, 2, 3, …} B. {0, 1, 2, 3, 4 …} C. {….-3, -2, -1, 0, 1, 2, 3…..}
4. Which statement best describes 16.23426… ?
A. It is a whole number but not an integer
B. It is an integer but not a rational number
C. It is a natural number but not a whole number
D. It is an irrational number but not a natural number
D. {-3, -2, -1, 0}
Putting it all together
Rational numbers can fit in _______ _______ _______ category.
What other things in the world can fit into more than one category?
 __________________ fit into the category ____________ and _______________

__________________ fit into the category ____________ and _______________

__________________ fit into the category ____________ and _______________
Real Numbers
________ number that I ________ now.
Rational Numbers
Ratio means __________
_______________________
_______ Numbers & their ___________ Opposites
_______________ Numbers
_____ plus all __________ ___________
Irrational Numbers
The prefix “IR-” means _______,
so IR-rational means
_____ ________
Decimals have….
 No ______
And
 No ________ _________
____________ Numbers
___________ Numbers
Go back to page 2 and label any numbers that are integers (i), whole numbers (w), or natural numbers (n)
HOMEWORK:
1. Finish labeling all the numbers on page 1 as rational (R) or irrational (IR)
2. Label any rational numbers that fit into the following categories: integers (i), whole
numbers (w), or natural numbers (n)
3. Complete all End of Course EOC-style multiple choice questions (on the next 2 pages)
End-Of-Course Exam Style Questions
Example 1 Which set below is the set of all integers?
A. {1, 2, 3, …….}
B. {0, 1, 2, 3, 4 …}
C.
{….-3, -2, -1, 0, 1, 2, 3…..} D.
{-3, -2, -1, 0}
Practice 1 Which set below is the set of all counting numbers?
A.
{1, 2, 3, …….}
B.{0, 1, 2, 3, 4 …}
C. {….-3, -2, -1, 0, 1, 2, 3…..}
Example 2 Which number below is not a rational number?
3
5
A.
B.
C. 0.111111……
5
5
Practice 2 Which statement best describes 2 ?
A. It is a whole number but not an integer
B. It is an integer but not a rational number
D.
D.
{-3, -2, -1, 0}
0.674
C. It is a natural number but not a whole number
D. It is an irrational number but not a natural
number
Example 3 Which set does not include 1,322?
A.
Integers
B. whole numbers
C. natural numbers
D. irrational numbers
C. natural numbers
D. real numbers
Practice 3 Which set does not include 0?
A.
integers
B. whole numbers
Practice 4 Which set only contains only whole numbers?
1 4
A.
{0, 3, 6, 7}
B. { 1, fff , ffff , 4} C. {2, 3, 5 , 8}
2 3
D. { -4, -1, 2, 9}
Practice 5 Which statement below is true?
A.
3
-3 is an integer B. -5 is a natural number C. ffff is an irrational number
4
Practice 6 Which name best describes the set of numbers? {0, 0.5, 1, 2, 4}
A. integers
B. whole numbers
C. natural numbers
D.
10 is a rational number
D. rational numbers
Practice 7 Which student provided the most accurate definition of the set of all integers?
A. Adam: “The set of all integers is all real numbers except fractions.”
B. Beth: “The set of all integers is all positive numbers and 0.”
C. Carline: “The set of all integers is all whole numbers and their negatives.”
D. Dave: “The set of all integers is decimals, fractions, and negatives.”
Practice 8 Which diagram shows the relationships between the sets of numbers?
Exit Slip Classifying Numbers Name ______________________ Date ________ Period ____
1. Which set contains only whole numbers?
A)
B)
C)
D)
2. Which of the following numbers is irrational?
{-3, -2, 1, 5, 8}
{0, 1, 2, 3, 4}
{9.3, 10.3, 11.3, 12.3}
{4, 6, 7 9}
A)
1.23232323…….
B) 4.23323222333….
C)
-5
D)
16
3. Circle all of the following that are rational numbers:
Fractions
Whole numbers
Natural numbers
7
4/4
Integers
Irrational numbers
decimals with a repeating pattern
2.44444
6.757261209873…
16
Exit Slip Classifying Numbers Name ______________________ Date ________ Period ____
1. Which set contains only whole numbers?
A)
B)
C)
D)
2. Which of the following numbers is irrational?
{-3, -2, 1, 5, 8}
{0, 1, 2, 3, 4}
{9.3, 10.3, 11.3, 12.3}
{4, 6, 7 9}
A)
1.23232323…….
B) 4.23323222333….
C)
-5
D)
16
3. Circle all of the following that are rational numbers:
Fractions
Whole numbers
Natural numbers
7
4/4
Integers
Irrational numbers
decimals with a repeating pattern
2.44444
6.757261209873…
16
Exit Slip Classifying Numbers Name ______________________ Date ________ Period ____
1. Which set contains only whole numbers?
A)
B)
C)
D)
2. Which of the following numbers is irrational?
{-3, -2, 1, 5, 8}
{0, 1, 2, 3, 4}
{9.3, 10.3, 11.3, 12.3}
{4, 6, 7 9}
A)
1.23232323…….
B) 4.23323222333….
C)
-5
16
D)
3. Circle all of the following that are rational numbers:
Fractions
Whole numbers
Natural numbers
7
4/4
Integers
Irrational numbers
decimals with a repeating pattern
2.44444
6.757261209873…
16