engineering mathematic

1 Engineering Mathematics 1 (AQB10102)

CHAPTER 1: NUMBERS AND ARITHMETIC
1.1 TYPE OF NUMBERS
NEGATIVE INTEGER

-

POSITIVE

AND

REAL NUMBERS (R)
•
•

Numbers that can be expressed as decimals Real Number System:
•
Consist of positive and negative natural numbers including 0
Example:
…, -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, …
•
All numbers including natural numbers, whole numbers, integers, rational numbers and irrational numbers are real numbers
Example:

4 = 4.0000...

−

5
= −0.8333...
6

1
= 0.5000...
2

• Classification of Real Numbers
Numbers
Example
Natural Numbers (N)
1, 2, 3, 4, 5, …
– counting numbers
Whole Numbers (W)
0, 1, 2, 3, 4, 5, …
– a set of zero together with the natural numbers
Rational Numbers (Q)
– any number that can be written in the form of

a b 8 0 5
, , ,7
4 9 3

where a and b are integers with b ≠ 0
a) Terminates: end in an infinite string ‘0’

3
= −0.75
4
65
= 65
1

−

b) Repeats: end with a block of digits that repeat over and over

Irrational Numbers (I)
- the decimal represented of irrational numbers do not repeat in cycles (pattern)

10
= 3.3333...
3
5
= 0.8333...
6

0.1010010000100001...
3 = 1.7320508075... log10 5 = 0.698970004336...

3 = 1.37050...
•

Real Numbers can be represented geometrically as points on a number line called
Real Line
Example

Prime Numbers
- any natural number, greater than 1, only divisible by itself and 1
Integers (Z)
– any positive and negative natural number including ‘0’
Zero
– the number represents ‘none’
‘nothing’
Even Numbers
– any number divisible by 2

SES

2,3, 5, 7,11,13,...

..., −3, −2, −1, 0,1, 2, 3,...

zero 0 or that

is

2, 4, 6,8,10,...

2 Engineering Mathematics 1 (AQB10102)
Odd Numbers
– any number that is not divisible by 2
Composite Numbers
– natural numbers but not a prime number

LOWEST COMMON MULTIPLY (LCM)

1, 3, 5, 7, 9,...