Numbers, Ratio and Rate, Financial Maths

NUMBER SYSTEMS

REAL NUMBERS (R) NON-REAL NUMBERS
All numbers represented on anumber negative numbers
line
All rational and irrational numbers



RATIONAL NUMBERS (Q) IRRATIONAL NUMBERS (Q)
Allfractions
Non-recurring and non-terminating
Any decimal that terminates or
recurs decimals

Allintegers, whole numbers and non perfect squares
natural numbers
non perfect cubes




INTEGERS (Z)
{..;-2; -1;0;1;2; ... )




WHOLE NUMBERS (No)
{0;1;2;3; .. )


NATURAL NUMBERS (N)
{1;2;3;4; ...)

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, RATIONAL NUMBERS
KaTional numbers are numbers thot can be written as a where aand
frGCIi
bare integers, but b0.
Example: -2=;0,333333
1 - : 0,=i;-7
2
2

10


IRRATIONAL NUMBERS
We knowthat the v1= 1 and v4 =2
:. surely N3 has a value between 1 and 2? So, V3 = 1,...
And since 3 is closer to 4 than 1, maybe 3 is closer to 2 than 1.
Check on your calculator.
Now, let's find the position of v3 on the number line.


1 2
1.73


V3 =1,732050808...calculator
V3 1,73 (correct to 2 decimal digits)
So, this number does exist - it is REAL!
But,we can only get an approximate value of it.Notice howthe digits after the
decimal have no pattern at all and go on and on.

Irrational numbers are infinite, NON-RECURRING (no pattern) decimals.

ACTIVITY 1
Complete the following table by ticking ()and crossing (x) the correct
column(s):
Simplify the nurnber first, if necessary.
NUMBER IR Q' No N

3,14159

22
7
-5
1.121122111..

3|PaRe

, No N
NUMBER R
0,333..
49
|25


-10
-2
/o,008
V9

We carn use an inequality symbol to represent sets of numbers in Maths

Example:

List the set of numbers represented by each of the following inequalities:

a) X<6,x ENo
2



b) x<5:xEN
I;2, 3;4,5

c) -4<x<1:xeZ
Interval
notodn
-4, 3,-2, -,0. -42
(only
reealo )
usebroc
kels
d) What about the following? X> 2;xE R


tion
el buldet notati
)
3
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