, Algebra
Numbers
Before you can start anything in mathematics you need to know how numbers work So here
are the basics There is a summary on the next page if you prefer flow diagrams
Numbers are broken down into Real and Non"Real numbers
• Non"Real R’ numbers are numbers that don’t exist imaginary or complex numbers
for example$ the square"root of a negative number like√−3 These numbers will give an
error on the calculator On the SHARP El",-, the calculator will say Error .
Calculation
• Real Numbers R are numbers that do exist They are broken down into Rational and
irrational numbers
o Irrational Numbers Q’ are numbers that don’t make sense I like to pretend they
are like my grandmother she likes to talk and talk but she doesn’t make any
sense In the same way2 irrational numbers go on and on called non"
terminating and they don’t have a pattern or make sense called non"recurring
An example of an irrational number is √7 = 2,645751311 … " do you see that it
doesn’t have a pattern and it doesn’t stop3
o Rational numbers on the other hand are either recurring that means they have a
pattern for example 42------ or they are terminating that means they end
for example .2., or - Rational numbers can be written as a fraction Rational
numbers are also broken down into$
Whole numbers N4 these are numbers that start at zero 4 and count
up in wholes2 e g 42 72 .2 - etc They DO NOT have decimals or
fractions A nice way to remember whole numbers start with zero is that
there is an 4 in whO
Ole
, Natural numbers N these are counting numbers which means that
they start at one 7 and count up in wholes2 e g 72 .2 - etc They do
NOT have decimals or fractions A nice way to remember that natural
numbers start with one is that there is a 7 in Natura77
Integers Z are positive and negative whole numbers2 e g "-2 ".2 "72
42 72 .2 - etc They also do NOT have fractions or decimals
Numbers
Real Numbers
Non-real numbers
• Don’t exist
• Give an error on your Rational Irrational
calculator.
• Terminating • Like granny
• E.g. square-root of a
• Or recurring • Non-recurring
negative number
• Can be written as • Non-terminating
a fraction.
Integers
Whole Numbers Natural Numbers • Positive and
• Start at zero • Start at one negative whole
• No decimals or • No decimals or numbers
fractions fractions • No fractions or
decimals.
: remember to learn both the names and the symbols because a question can use either the
symbols or the names
, Activity 7
7 Tick the correct columns in the table below$
Number Real Non"
Non"Real Rational Irrational Whole Natural Integer
4
"7
"72;,
√3
√−8
√−5
. Given the equation$ 0 = +3 2 −5 +6
Solve for when is
a real
b non"real
c an integer
Rounding Off
Part of knowing your numbers is remembering the facts about rounding off so here is some
quick revision for you$
When you round off check how many places you want to round off to2 then look at the number
next to the last number you will have once you have rounded off →
e g round off to three decimal places$ 42 7.-;,=
place rounding off to number you use to decide whether the
number next door goes up or stays the same
If the number is , or bigger than , that is =2
>2 ?2 @ then the number next door goes up
If the number is smaller than , that is ;2 -2
.2 72 4 the number next door stays the
same
Numbers
Before you can start anything in mathematics you need to know how numbers work So here
are the basics There is a summary on the next page if you prefer flow diagrams
Numbers are broken down into Real and Non"Real numbers
• Non"Real R’ numbers are numbers that don’t exist imaginary or complex numbers
for example$ the square"root of a negative number like√−3 These numbers will give an
error on the calculator On the SHARP El",-, the calculator will say Error .
Calculation
• Real Numbers R are numbers that do exist They are broken down into Rational and
irrational numbers
o Irrational Numbers Q’ are numbers that don’t make sense I like to pretend they
are like my grandmother she likes to talk and talk but she doesn’t make any
sense In the same way2 irrational numbers go on and on called non"
terminating and they don’t have a pattern or make sense called non"recurring
An example of an irrational number is √7 = 2,645751311 … " do you see that it
doesn’t have a pattern and it doesn’t stop3
o Rational numbers on the other hand are either recurring that means they have a
pattern for example 42------ or they are terminating that means they end
for example .2., or - Rational numbers can be written as a fraction Rational
numbers are also broken down into$
Whole numbers N4 these are numbers that start at zero 4 and count
up in wholes2 e g 42 72 .2 - etc They DO NOT have decimals or
fractions A nice way to remember whole numbers start with zero is that
there is an 4 in whO
Ole
, Natural numbers N these are counting numbers which means that
they start at one 7 and count up in wholes2 e g 72 .2 - etc They do
NOT have decimals or fractions A nice way to remember that natural
numbers start with one is that there is a 7 in Natura77
Integers Z are positive and negative whole numbers2 e g "-2 ".2 "72
42 72 .2 - etc They also do NOT have fractions or decimals
Numbers
Real Numbers
Non-real numbers
• Don’t exist
• Give an error on your Rational Irrational
calculator.
• Terminating • Like granny
• E.g. square-root of a
• Or recurring • Non-recurring
negative number
• Can be written as • Non-terminating
a fraction.
Integers
Whole Numbers Natural Numbers • Positive and
• Start at zero • Start at one negative whole
• No decimals or • No decimals or numbers
fractions fractions • No fractions or
decimals.
: remember to learn both the names and the symbols because a question can use either the
symbols or the names
, Activity 7
7 Tick the correct columns in the table below$
Number Real Non"
Non"Real Rational Irrational Whole Natural Integer
4
"7
"72;,
√3
√−8
√−5
. Given the equation$ 0 = +3 2 −5 +6
Solve for when is
a real
b non"real
c an integer
Rounding Off
Part of knowing your numbers is remembering the facts about rounding off so here is some
quick revision for you$
When you round off check how many places you want to round off to2 then look at the number
next to the last number you will have once you have rounded off →
e g round off to three decimal places$ 42 7.-;,=
place rounding off to number you use to decide whether the
number next door goes up or stays the same
If the number is , or bigger than , that is =2
>2 ?2 @ then the number next door goes up
If the number is smaller than , that is ;2 -2
.2 72 4 the number next door stays the
same
