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Real Number System – Classifying
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5
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Date: __________
Algebra I Common Core
Sheet #01 -01
Classify each of the numbers in the chart below by checking each set that the number belongs to.
Which of the following numbers is an
irrational number?
(1)
5.38
(3)
(2)
̅̅̅
0. ̅63
(4)
7
𝜋
2
-5
All of the following numbers belong to the set
of integers except:
(1)
-5
(3)
-2.7
(2)
2
(4)
0
8
All of the following belong to the set of
irrational numbers except:
(1)
2𝜋
(3)
(2)
−2. 3̅
(4)
√8
𝜋
4
Which set contains the number 5𝜋?
(1)
Integers
(3)
Rational
(2)
Irrational
(4)
Natural
Which is a rational number?
(1)
√16
(3)
𝜋
(2)
√15
(4)
√20
9
Which one of the following numbers is not
irrational?
(1)
√16
(3)
𝜋
(2)
-√46
(4)
√21
Which of the following numbers belongs to
the set of whole numbers?
(1)
-9
(3)
6
3
(2)
5
3
(4)
1.5
Which of the following is not always true?
(1)
The product of two irrational numbers is
irrational.
(2)
The product of two rational numbers is
rational.
(3)
The sum of two rational numbers is
rational.
(4)
The sum of a rational number and an
irrational number is irrational.
10 If a statement is made using the word ALL or
ALWAYS, you can prove the statement false
by providing a counterexample, an example
that shows that a conjecture (idea) is false.
State whether the following conjecture is true
or false. If false, provide a counterexample.
All square roots are irrational numbers
12 Given:
L = √2
M = 3√3
N = √16
P = √9
Determine whether the following expressions
result in a rational or irrational number.
Justify your response.
(A)
L+M
(B)
M+N
(C)
N+P
(D)
P+L
11 Determine whether the following statements
are always, sometimes, or never true. If a
statement is not always true, give a
counterexample.
(A)
Integers are rational numbers.
(B)
Rational numbers are integers.
(C)
The product of a rational number and an
irrational number is irrational.
(D)
All whole numbers are always counting
numbers.
13 The formula 𝑠 = √15𝑑 relates the length of a
(E)
Every counting number is also an integer.
skid mark, d, with the speed the car was
traveling, s. If you solved the equation, would
s be rational or irrational when d = 15?
Justify your response.