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173-1592212488562-HND MAT W1 Preliminary Lessons (Part 01)

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Unit 11 – Maths for Computing
2. PRELIMINARY LESSONS
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2. Preliminary Lessons
2.1 Numbers
2.2 Number Systems
2.3 Algebra
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2.1 Numbers
2.1.1 Types of Numbers
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2.1 Numbers
2.1.1 Types of Numbers
4
2.1 Numbers
2.1.1 Types of Numbers
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2.1 Numbers
2.1.1 Types of Numbers
1
= 0.5 − π‘‡π‘’π‘Ÿπ‘šπ‘–π‘›π‘Žπ‘‘π‘–π‘›π‘” π‘π‘’π‘šπ‘π‘’π‘Ÿ
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1
3
= 0.3333 … = 0. 3ሢ − π‘…π‘’π‘π‘’π‘Ÿπ‘Ÿπ‘–π‘›π‘” π‘…π‘’π‘π‘’π‘Žπ‘‘π‘–π‘›π‘” π‘π‘’π‘šπ‘π‘’π‘Ÿ
ሢ 3ሢ − π‘…π‘’π‘π‘’π‘Ÿπ‘Ÿπ‘–π‘›π‘” π‘…π‘’π‘π‘’π‘Žπ‘‘π‘–π‘›π‘” π‘π‘’π‘šπ‘π‘’π‘Ÿ
1.413413413 … = 1. 41
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2.1 Numbers
2.1.1 Types of Numbers
πœ‹
22
= 3.142 …
7
−
π‘π‘œπ‘› − π‘‘π‘’π‘Ÿπ‘šπ‘–π‘›π‘Žπ‘‘π‘–π‘›π‘” π‘œπ‘Ÿ π‘π‘œπ‘› − π‘Ÿπ‘’π‘π‘’π‘Ÿπ‘Ÿπ‘–π‘›π‘” π‘π‘œπ‘› − π‘Ÿπ‘’π‘π‘’π‘Žπ‘‘π‘–π‘›π‘” π‘π‘’π‘šπ‘π‘’π‘Ÿ
2 = 1.414 …
−
π‘π‘œπ‘› − π‘‘π‘’π‘Ÿπ‘šπ‘–π‘›π‘Žπ‘‘π‘–π‘›π‘” π‘œπ‘Ÿ π‘π‘œπ‘› − π‘Ÿπ‘’π‘π‘’π‘Ÿπ‘Ÿπ‘–π‘›π‘” π‘π‘œπ‘› − π‘Ÿπ‘’π‘π‘’π‘Žπ‘‘π‘–π‘›π‘” π‘π‘’π‘šπ‘π‘’π‘Ÿ
3 = 1.732 …
−
π‘π‘œπ‘› − π‘‘π‘’π‘Ÿπ‘šπ‘–π‘›π‘Žπ‘‘π‘–π‘›π‘” π‘œπ‘Ÿ π‘π‘œπ‘› − π‘Ÿπ‘’π‘π‘’π‘Ÿπ‘Ÿπ‘–π‘›π‘” π‘π‘œπ‘› − π‘Ÿπ‘’π‘π‘’π‘Žπ‘‘π‘–π‘›π‘” π‘π‘’π‘šπ‘π‘’π‘Ÿ
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2.1 Numbers
2.1.1 Types of Numbers
1 = 1.0 , −1 = −1 . 0 , 0 = 0.0
− π‘‡π‘’π‘Ÿπ‘šπ‘–π‘›π‘Žπ‘‘π‘–π‘›π‘” π‘π‘’π‘šπ‘π‘’π‘Ÿs
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2.1 Numbers
2.1.1 Types of Numbers
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2.1 Numbers
2.1.1 Types of Numbers
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2.1 Numbers
2.1.1 Types of Numbers
Positive Integers with Zero. Integers ≥ 0
Negative Integers. Integers < 0
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2.1 Numbers
2.1.1 Types of Numbers
Positive Integers with Zero. Integers ≥ 0
Negative Integers. Integers < 0
Integers > 0
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2.1 Numbers
2.1.1 Types of Numbers
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2.1 Numbers
2.1.1 Types of Numbers
π‘…π‘’π‘Žπ‘™ π‘π‘’π‘šπ‘π‘’π‘Ÿπ‘  − ℝ
π‘…π‘Žπ‘‘π‘–π‘œπ‘›π‘Žπ‘™ π‘π‘’π‘šπ‘π‘’π‘Ÿπ‘  − β„š
πΌπ‘›π‘‘π‘’π‘”π‘’π‘Ÿπ‘  − β„€
π‘Šβ„Žπ‘œπ‘™π‘’ π‘π‘’π‘šπ‘π‘’π‘Ÿπ‘  − W
π‘ƒπ‘œπ‘ π‘–π‘‘π‘–π‘£π‘’ πΌπ‘›π‘‘π‘’π‘”π‘’π‘Ÿπ‘  π‘€π‘–π‘‘β„Ž π‘π‘’π‘Ÿπ‘œ − β„€0+
π‘π‘Žπ‘‘π‘’π‘Ÿπ‘Žπ‘™ π‘π‘’π‘šπ‘π‘’π‘Ÿπ‘  − β„•
π‘ƒπ‘œπ‘ π‘–π‘‘π‘–π‘£π‘’ πΌπ‘›π‘‘π‘’π‘”π‘’π‘Ÿπ‘  − β„€+
π‘π‘’π‘”π‘Žπ‘‘π‘–π‘£π‘’ πΌπ‘›π‘‘π‘’π‘”π‘’π‘Ÿπ‘  − β„€−
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2.1 Numbers
2.1.1 Types of Numbers
Special Types of Numbers
β–ͺ Odd and Even Numbers
β–ͺ Odd Numbers – Numbers that are not divisible by 2. Always the remainder is 1.
Ex : 1,3,5,7,9, …
β–ͺ Even Numbers – Numbers that are divisible by 2. Always the remainder is 0.
Ex : 2,4,6,8,10, …
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2.1 Numbers
2.1.1 Types of Numbers
Special Types of Numbers
β–ͺ Squared Numbers
β–ͺ Numbers that are created by squaring a number.
Ex :
12 = 1x1 = 1
(-1)2 = (-1)x(-1) = 1
22 = 2x2 = 4
(-2)2 = (-2)x(-2) = 4
52 = 5x5 = 25
(-5)2 = (-5)x(-5) = 25
102 = 10x10 = 100
(-10)2 = (-10)x(-10) = 100
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2.1 Numbers
2.1.1 Types of Numbers
Special Types of Numbers
β–ͺ Prime Numbers
β–ͺ Numbers that are only divisible by 1 and itself.
Ex :
2,3,5,7,11,13,17,19, …
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2.1 Numbers
2.1.2 The Number Line
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2.1 Numbers
2.1.3 BODMAS Theory
β–ͺ Order of Mathematical Operations
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2.1 Numbers
2.1.3 BODMAS Theory
Examples
i.) 4 - 3 + 6 x 1
ii.) 4 - (3 + 6) x 1
iii.) 8 ÷ 2 + 10 ÷ 5
iv.) 5 + (21 - 3) ÷ 6 x 3
v.) 22 + 6 – 4 ÷ 2
vi.) { 8 - [5 + (4 x 2)] } + 6
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2.1 Numbers
2.1.3 BODMAS Theory
Examples
i.) 4 - 3 + 6 x 1
=4-3+6
=1+6
=7
ii.) 4 - (3 + 6) x 1
=4-9x1
=4-9
= (-5)
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2.1 Numbers
2.1.3 BODMAS Theory
Examples
iii.) 8 ÷ 2 + 10 ÷ 5
= 4 + 10 ÷ 5
=4+2
=6
iv.) 5 + (21 - 3) ÷ 6 x 3
= 5 + 18 ÷ 6 x 3
=5+3x3
=5+9
= 14
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2.1 Numbers
2.1.3 BODMAS Theory
Examples
v.) 22 + 6 – 4 ÷ 2
=4+6–4÷2
=4+6-2
= 10 - 2
=8
vi.) { 8 - [5 + (4 x 2)] } + 6
= { 8 - [5 + 8] } + 6
= { 8 - 13} + 6
= (-5) + 6
=1
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Summary
2. Preliminary Lessons
2.1 Numbers
2.1.1 Types of Numbers
2.1.2 The Number Line
2.1.3 BODMAS Theory
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END OF THE SESSION
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