Revision Notes
Class-9 Mathematics
Chapter 1 – Number Systems
• Real numbers and imaginary number together form number systems.
• We will discuss imaginary numbers in higher classes, let us restrict our
discussion to real numbers
• Real numbers are the set of natural numbers, whole numbers, integers,
rational and irrational numbers. Denoted by R
• Natural numbers:
• These are counting numbers from starting from 1 .
• The set 1,2,3,4,5,6,7.... is called natural numbers.
• Denoted by N
• Whole numbers:
• These are the set of natural numbers including 0 .
• The set 0,1,2,3,4,5,6.... is called whole numbers.
• Denoted by W
• Integers:
• These are the set of negative numbers, positive numbers and 0
excluding fractions.
• The set .... − 3, −2, −1,0,1,2,3.... is called integers.
• Denoted by Z
• Rational numbers:
• These are those number which can be expressed in the form of fraction
p
i.e., where p and q are integers and q 0 .
q
3 −2 −3
• For example: , , , etc.
5 9 4
• Denoted by Q
• There are infinitely many rational numbers between any two rational
numbers.
• Irrational numbers:
• These are those which are not rational i.e., which cannot be expressed
Class IX Mathematics www.vedantu.com 1
Class-9 Mathematics
Chapter 1 – Number Systems
• Real numbers and imaginary number together form number systems.
• We will discuss imaginary numbers in higher classes, let us restrict our
discussion to real numbers
• Real numbers are the set of natural numbers, whole numbers, integers,
rational and irrational numbers. Denoted by R
• Natural numbers:
• These are counting numbers from starting from 1 .
• The set 1,2,3,4,5,6,7.... is called natural numbers.
• Denoted by N
• Whole numbers:
• These are the set of natural numbers including 0 .
• The set 0,1,2,3,4,5,6.... is called whole numbers.
• Denoted by W
• Integers:
• These are the set of negative numbers, positive numbers and 0
excluding fractions.
• The set .... − 3, −2, −1,0,1,2,3.... is called integers.
• Denoted by Z
• Rational numbers:
• These are those number which can be expressed in the form of fraction
p
i.e., where p and q are integers and q 0 .
q
3 −2 −3
• For example: , , , etc.
5 9 4
• Denoted by Q
• There are infinitely many rational numbers between any two rational
numbers.
• Irrational numbers:
• These are those which are not rational i.e., which cannot be expressed
Class IX Mathematics www.vedantu.com 1
