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JMAP Solutions – NUMBERS OPERATIONS AND PROPERTIES: Classifying Numbers
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CLASSIFYING NUMBERS
MATH A APPEARANCES:
MATH B APPEARANCES:
069923a, 080432a, 010632a 2-pointer
060003a, 060120a, 080102a, 010219a, 060211a, 080208a
060303a, 010416a, 080523a, 080718a multiple choice
060813b multiple choice
REGENTS QUESTIONS
SOLUTIONS
080208a
The number 0.14114111411114 . . . is
irrational because it may not be
expressed as the ratio of two integers.
It is not a repeating decimal.
1
The number 0.14114111411114 . . . is
(1) integral
(3) irrational
(2) rational
(4) whole
2
π is an irrational number because it
may not be expressed as the ratio of
Write an irrational number and explain
two integers.
why it is irrational.
010632a
3
069923a
Which number below is irrational?
4
, 20, 121
9
Why is the number you chose an
irrational number?
4
010416a
Which number is irrational?
(1) 9
(3) 0.3333
2
(2) 8
(4)
3
5
4 2

9 3
121 
11
1
(2)
8 is irrational because it may not be
expressed as the ratio of two integers.
9
3
1
0.3333 
3333
10000
(1)
2 is irrational because it may not be
Which expression represents an irrational
expressed as the ratio of two integers.
number?
060303a
2
(1)
(2)
6
20 is irrational because it may not be
expressed as the ratio of two integers.
1
2
(3) 0.17
(4) 0
0.17 
17
100
(3)
0
0
1
JMAP Solutions – NUMBERS OPERATIONS AND PROPERTIES: Classifying Numbers
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010219a
Which is an irrational number?
(1) 9
(3) 3
3
(2) 3.14
(4)
4
7
060211a
Which is an irrational number?
1
(1) 0
(3) 
3
(2)  
(4) 9
8
080523a
Which is an irrational number?
(1) 0.3
(3) 49
3
(2)
(4) 
8
9
080718a
Which number is irrational?
5
(1)
(3) 121
4
(2) 0. 3
(4) π
10
080432a
99
, 164, 196
11
Identify the expression that is a rational
number and explain why it is rational.
Given:
11
060813b
The value of x 2  9 is a real and
irrational number when x is equal to
(1) 5
(3) -3
3 is irrational because it may not be
expressed as the ratio of two integers.
9
3
314
3.14 
1
100
(2)
π is an irrational number because it
may not be expressed as the ratio of
two integers.
0
0
1
9
3
1

1 1

3 3
(4)
π is an irrational number because it
may not be expressed as the ratio of
two integers.
0.3 
1
3
49 
7
1
(4)
π is an irrational number because it
may not be expressed as the ratio of
two integers.
0.3 
1
3
121 
11
1
14
, which is rational, because
1
it is the ratio of two integers.
196 
99
 3,
11
99
3
11
(4)
x  9  42  9  7
2
JMAP Solutions – NUMBERS OPERATIONS AND PROPERTIES: Classifying Numbers
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(2) 0
(4) 4
12
060003a
Which number is rational?
(1) π
(3) 7
(2)
5
4
(4)
13
3
2
060120a
Which is a rational number?
(1) 8
(3) 5 9
(2) 
(4) 6 2
14
080102a
Which expression is rational?
(1)  
(3) 3
(2)
1
2
(4)
1
4
(2)
5
is rational because it is the ratio of
4
two integers.
(3)
5 9 is rational because it is the ratio
15
of two integers,
.
1
(4)
1 1
 , the ratio of two integers.
4 2