MB0901 QR

In this document you can review important
• Definitions
• Facts
• Formulae
• Procedures
Class – IX, CBSE MB0901: The Number System
Learn Math for Free. Visit www.ganitgurooz.com

What is a Rational
Number?
Class – IX,CBSE MB0901: The Number System
Important Definitions
Topic: Rational Numbers

What is a Rational
Number?
A number is called a rational number,
if it can be written in the form ,
where and are integres and 0.
r
p
q
p q q

What is an
Irrational Number?
Topic: Irrational Numbers

What is an
Irrational Number?
A number is called a irrational number,
if it cannot be written in the form ,
where and are integres and 0.
s
p
q
p q q

What is the nth root
of a number x?

What is the nth root
of a number x?
The root of a number ,
is a number , if .
th
n
n x
y y x

Fact # 1
The decimal expansion of a rational number is either terminating
or non-terminating recurring.
Important Facts

Fact # 2
A number whose decimal expansion is either terminating or
non-terminating recurring is a rational number.
Important Facts

Fact # 3
The decimal expansion of an irrational number is non-terminating
non-recurring.
Important Facts

Fact # 4
A number whose decimal expansion is non-terminating
non-recurring is an irrational number.
Important Facts

Fact # 5
All the rational numbers and irrational numbers taken together
makes up the collection of real numbers.
Important Facts
Topic: Real Numbers

Fact # 6
Every point on the number line represents one and only one real
number.
Important Facts
Topic: Real Numbers

Fact # 7
Every real number has a unique location on the real line.
Important Facts
Topic: Real Numbers

Fact # 8
The sum of a non-zero rational number and an irrational number
is an irrational number.
Important Facts

Fact # 9
The difference of a non-zero rational number and an irrational
number is an irrational number.
Important Facts

Fact # 10
The product of a non-zero rational number and an irrational
number is an irrational number.
Important Facts

Fact # 11
The ratio of a non-zero rational number and an irrational number
is an irrational number.
Important Facts

Fact # 12
The Pythagorean theorem states that in a right angled triangle, the
square of the hypotenuse is equal to the sum of the squares of the
other two sides.
Important Facts
Topic: Pythagoras’ Theorem

Important Formulae
For positive real numbers and , the following identities hold:a b
2
2
i ii
iii iv
v 2
a a
ab a b
b b
a b a b a b a b a b a b
a b a ab b

Important Formulae
Let 0 be a real number and and be rational numbers. Thena p q
i ii
iii iv
qp q p q p pq
p
pp q p p
q
a a a a a
a
a a b ab
a

How to Locate an irrational number on the number line?
Important Procedures
n

n
: Locate the point on the number line.Call it A.nStep1

n
: Drawa perpendicularABof length1unitatthepoint A.Step2

n
:Jointheorigin 0 tothepointB.Thislengthisequalto .nStep3

n
:Withcenteratorigin,andradiusOB,drawanarcintersectingthereallineatP.Step4

n
:Withcenteratorigin,andradiusOB,drawanarcintersectingthereallineatP.Step4
:The point P denotes on the number line.Step5

How to represent a terminating decimal (p.ab) on the
number line through successive magnification?

:Locatethepointponthenumberline.Step1

:Locatethepointponthenumberline.
:Dividetheunitlength , 1 into10equalparts.p p
Step1
Step2

:Dividetheunitlength , 1 into10equalparts.
:Countaanda+1partsstartingfromp.Thesearepoints and 1
p p
p a p a
Step1
Step2
Step3

:Magnifythelength , 1
p p
p a p a
p a p a
Step1
Step2
Step3
Step4

:Divide this leng
p p
p a p a
p a p a
Step1
Step2
Step3
Step4
Step5 th into 10 equal parts.

:Divide this leng
p p
p a p a
p a p a
Step1
Step2
Step3
Step4
:Countbpartsstartingfrom p aStep6

:Divide this leng
p p
p a p a
p a p a
Step1
Step2
Step3
Step4
:Countbpartsstartingfrom
:Thispointrepresents
p a
p ab
Step6
Step7

How to write a recurring decimal as a ratio of integers?

:Assume the given number as x.Step1

:Assume the given number as x.
:Let umber of digits to the right of the decimal that do not form a part of the recurring string.n n
Step1
Step2

:Let umber of digits to the right of the decimal that do not form a part of the recurring string.
:Let ength of the recurring string of digits.
n n
m l
Step1
Step2
Step3

:Fin
n n
m l
Step1
Step2
Step3
Step4 d10n
x

:Fin
n n
m l
Step1
Step2
Step3
Step4 d10
:Find10
n
m n
x
xStep5

:Fin
n n
m l
Step1
Step2
Step3
Step4 d10
:Find10
:Find10 10
n
m n
m n n
x
x
x x
Step5
Step6

:Fin
n n
m l
Step1
Step2
Step3
Step4 d10
:Find10
:Find10 10
:Divide the integer you get by10 10 to get the required rational form of the number x.
n
m n
m n n
m n n
x
x
x x
Step5
Step6
Step7

How to Rationalize an irrational denominator?

How to Rationalize an irrational denominator?
Form of Denominator Rationalising Factor Denominator of Rationalised
Form
a a a
a b a b 2
a b
a b a b a b
m a n b m a n b 2 2
m a n b

MB0901 QR

Recommended

Recommended

More Related Content

Viewers also liked

Viewers also liked (19)

More from GanitGurooz2013

More from GanitGurooz2013 (6)

Recently uploaded

Recently uploaded (20)

MB0901 QR