7480 Demonstrate understanding of rational and irrational numbers and number systems v 2021

Welcome

Demonstrate understanding of rational and
irrational numbers and number systems
Unit Standard 7480

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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).

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2

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.

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3

Answer True or False to the following:
‘The natural numbers are a subset of the integers’.

TRUE
FALSE

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4

The Rational numbers are…….

A. Any number of the form , where p, q ∈ ℤ and q≠0.


B. Any number of the form , where p, q ∈ ℤ .


C. Any number of the form , where p, q ∈ ℕ .


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Which number is not a rational number?

A. 0.3 Terminating
Decimal
B.
Terminating
Decimal
C. -1
Terminating
Decimal
D. Decimal
Terminating expansion that
Decimal
can go on
E. 0. ሶ Recurring forever
Decimal without
recurring
F. =1.41421356237..

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Consider whether the following statements are
True or False?

Statement True or False
False
Every integer is a natural number True

Every natural number is a rational number

Every rational number is an integer False
Every integer is a rational number True
Every natural number is an integer True

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Venn Diagram & Number Line ℕ, ℤ and ℚ.

Page 23

Natural
ℕ

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Venn Diagram & Number Line ℕ, ℤ and ℚ.

Integers Page 23
ℤ

ℤ\ℕ

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Venn Diagram & Number Line ℕ, ℤ and ℚ.

Rational Page 23
ℚ

ℚ\ℤ

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Rational Page 23
ℚ

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Rational Page 23
ℚ

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Student Activity 1 Calculator Activity
Calculator/ Decimals
Number

(1) 4

(2) 9ൗ100

(3) 4ൗ9

(4) 25ൗ36

(5) 2
(6) 8
(7) 3 5
(8)
(9) 1- 2

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Student Activity 1 Calculator Activity

Number Calculator/ Decimals

(1) 4 2 Rational
3
(2) 9ൗ100 0.130 Terminating
2 Or
(3) 4ൗ9
0.356ሶ Recurring
(4) 25ൗ36
6 Irrational
(5) 2 0.832ሶ
(6) 8 Decimal
(7) 3 5 22 expansion that
(8)
(9) 1- 2 1.4142135623..7..309504…. can go on
forever
22..882824827412247714621590…09. … . without
11..7709099759974656197.64767906…9181-9.…7.25947 recurring

© GMLS 33..11414519256954325…68.957493…23.….

14 -0.414213562-03.74419472911325.…624…

What is a Surd?

A Surd is an irrational number
containing a root term.

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Number Calculator/ Decimals Irrational Surd
4 2

9ൗ100 0.3
4ൗ9 2
3
25ൗ36 0.65ሶ
6
2
0.83ሶ
8
35 2

1- 2 1.421√42213562

1.709975947
2.828427125



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16 -0.414211-352624

Irrational Numbers Familiar
irrationals

23 5 7

Rational Page 23
ℚ

Are these the only irrational numbers
based on these numbers?

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23 5 7

Rational Page 23
ℚ






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The set of Rational and Irrational numbers together make up the Real

number system (ℝ).

Real +
ℝ
Rational

ℚ

Irrational Numbers Type equation here.

ℝ\ℚ

−

−

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Student Activity

Classify all the following numbers as natural, integer, rational, irrational or real using the
table below. List all that apply.

5 Natural Integer Rational Irrational Real
ℕ ℤ ℚ ℝ\ℚ ℝ
1+ 2
−9.6403915 …     
 
−1    
  
2  
 
6.3ሶ 6ሶ  
2  
-3 
38 
0

-3 

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The diagram represents the sets: Natural Numbers ℕ, Integers ℤ, Rational
Numbers ℚ Real Numbers ℝ.

Insert each of the following numbers in the correct place on the diagram:

5, 1 + 2, −9.6403915. . … , − 1 , 6.3ሶ 6ሶ , 2 , -3, 3 8, 0 and - 3.
2

ℝℚ
ℚ ℤ ℕℕ

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The diagram represents the sets: Natural Numbers ℕ, Integers ℤ, Rational
Numbers ℚ Real Numbers ℝ.

Insert each of the following numbers in the correct place on the diagram:

5, + , − . . . … , − , 6. ሶ ሶ , 2 , -3, , 0 and - .


ℝ ℚ ℤ ℕ
1+ -3
6. ሷ
0 5
−


- -9.6403915…

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Questions
& Answers

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