This is a set of notes that teach, contain summaries and have example questions (with answers and corrections) about numbers (rational, irrational etc.), ratio and rate, and financial maths. This set helps you understand more in depth on these subjects. Although it is in the syllabus for grade 9, t...
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; ...)
2|ae
, 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
4|?e
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