Transcript Student quiz on number systems - from workshop 10

Assessment
Quiz
Time…………
The
Natural
numbers are…..
A.
The set of all whole numbers , positive, negative and 0.
B.
The set of all positive whole numbers (excluding 0).
C.
The set of all positive whole numbers (including 0).
The Integers are……
A.
The set of all whole numbers , positive, negative and 0.
B.
The set of all positive whole numbers only.
C.
The set of all negative whole numbers only.
Answer True or False to the following:
‘The natural numbers are a subset of the integers’.
TRUE
FALSE
The Rational numbers are…….
𝒑
𝒒
A.
Any number of the form , where p, q ∈ ℤ and q≠0.
𝒒
B.
Any number of the form
𝒑
,
𝒒
Any number of the form
𝒑
, where
𝒒
C.
where p, q ∈ ℤ .
p, q ∈ ℕ .
Which number is not a rational number?
A.
0.3
Terminating
Decimal
B.
𝟐
𝟓
Terminating
Decimal
C.
𝟑
-1
𝟒
Terminating
Decimal
D.
E.
F.
𝟏𝟔
0.𝟏
Terminating
Decimal
Recurring
Decimal
𝟐 =1.41421356237..
Decimal
expansion that
can go on
forever
without
recurring
Consider whether the following statements
are True or False?
Statement
True or False
Every integer is a natural number
False
Every natural number is a rational number
True
Every rational number is an integer
False
Every integer is a rational number
True
Every natural number is an integer
True
ℕ, ℤ and ℚ.
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Venn Diagram & Number Line
Natural
ℕ
Integers
ℤ
ℤ\ℕ
ℕ, ℤ and ℚ.
Page 23
Venn Diagram & Number Line
ℕ, ℤ and ℚ.
Page 23
Venn Diagram & Number Line
Rational
ℚ
ℚ\ℤ
Rational
ℚ
𝟑
𝟐
𝟒
𝟐
𝟓
𝟐
𝟔
𝟐
Page 23
𝟐
𝟐
Rational
ℚ
Page 23
𝟒 𝟓 𝟔 𝟕 𝟖 𝟗 𝟏𝟎 𝟏𝟏 𝟏𝟐
𝟒𝟒 𝟒 𝟒 𝟒𝟒 𝟒 𝟒 𝟒
Student Activity 1
Calculator Activity
Number
(1)
(2)
4
9
100
(3)
4
(4)
25
9
36
(5)
2
(6)
8
(7)
3
5
(8)
𝜋
(9)
1- 2
Calculator/ Decimals
Student Activity 1
Calculator Activity
Number
(1)
(2)
4
9
100
(3)
4
(4)
25
9
36
(5)
2
(6)
8
(7)
3
5
(8)
𝜋
(9)
1- 2
Calculator/ Decimals
2
Rational
3
0.3
Terminating
10
Or
2
0.6
Recurring
3
5
0.83
6
Irrational
1.414213562....2
1.41421356237309504….
Decimal
2.828427125….
2.82842712474619009….
2 2
expansion
1.70997594667669681….
1.709975947….
1.709975947 that can go
on forever
without
3.14159265358979323….
3.141592654….
𝜋
recurring
-0.41421356237497912.…
-0.4142135624…
1- 2
What is a Surd?
A Surd is an irrational
number containing a root term.
Number
4
9
100
4
25
3
9
36
Calculator/
Decimals
2
0.3
2
3
5
0.83
6
0.6
2
1.414213562
2
8
2.828427125
2√2
5
1.709975947
𝜋
1- 2
3.141592654
𝜋
-0.4142135624
1- 2
Irrational
Surd
Irrational Numbers
Familiar
irrationals
3
5
7𝑒
Rational
ℚ
Are these the only irrational numbers
based on these numbers?
𝜋
Page 23
2
𝟐
𝟐
𝟕
𝟐
Rational
𝟑
𝟓
ℚ
𝟐
𝟐
𝒆
𝟐
𝝅
𝟐
3
5
7𝑒
𝜋
Page 23
2
The set of Rational and Irrational numbers
together make up the Real number system (ℝ).
Real
ℝ
𝟖
𝟑+ 𝟓
Rational
ℚ
Irrational Numbers
ℝ\ℚ
Type equation here.
− 𝟏𝟏
𝝅
𝟏− 𝟐
Student Activity
Classify all the following numbers as natural, integer, rational,
irrational or real using the table below. List all that apply.
5
Natural
ℕ
Integer
ℤ
Rational
ℚ



Irrational
ℝ\ℚ
Real
ℝ

1+ 2


−9.6403915 …


1
−2


6.36


2

-3
3
8
0
- 3













The diagram represents the sets: Natural Numbers ℕ,
Integers ℤ, Rational Numbers ℚ 𝑎𝑛𝑑 Real Numbers ℝ.
Insert each of the following numbers in the correct place on the
diagram:
1
2
3
5, 1 + 2, −9.6403915. . … , − , 6.36 , 2𝜋, -3, 8, 0 and - 3.
ℝ
ℚ
ℚ
ℤ
ℕ
ℕ
The diagram represents the sets: Natural Numbers ℕ,
Integers ℤ, Rational Numbers ℚ 𝑎𝑛𝑑 Real Numbers ℝ.
Insert each of the following numbers in the correct place on the
diagram:
𝟏
−𝟗. 𝟔𝟒𝟎𝟑𝟗𝟏𝟓. . … , −
𝟐
5, 𝟏 + 𝟐,
ℝ
1+ 𝟐
ℚ
6.𝟑𝟔
𝟐𝝅
- 𝟑
, 6.𝟑𝟔, 2𝝅 , -3,
ℤ
𝟏
−
𝟐
ℕ
-3
0
-9.6403915…
𝟑
𝟑
𝟖
𝟖 , 0 and - 𝟑.
5