2. TYPES OF NUMBERS
• Natural Numbers (N)
• Whole Numbers (W)
• Integers (Z)
• Rational numbers (Q) and Irrational Numbers
• Real numbers (R)
3. RATIONAL NUMBERS AND DECIMALS
• Any number is known as rational number if it is
expressed as quotient or fraction pq. Of two
integers where p is the numerator and q is the
denominator. Since p and q are integers. So, q can
also be equal to 1. So, every integer is a rational
number.
• Some of the examples of rational number are ½,
1/5, 3/4
4. DECIMAL EXPANSION OF RATIONAL
NUMBER
• A rational number gives either terminating or non-
terminating recurring decimal expansion. Thus, we can
say that a number whose decimal expansion is
terminating or non-terminating recurring is rational.
• Decimal numbers with the finite number of digits are
called as terminating decimals while decimals with the
infinite number of digits are called as non-terminating
decimals.Example: 0.5, 2.456, 123.456, etc
5. IRRATIONAL NUMBERS
• An irrational number is a type of real number which
cannot be represented as a simple fraction. It
cannot be expressed in the form of a ratio. ...
Example: √2, √3, √5, √11, √21, π(Pi) are all
irrational.
6. OPERATIONS ON RATIONAL AND IRRATIONAL
NUMBERS
• When the addition or subtraction operation is done on a rational
and irrational number, the result is an irrational number.
• When the multiplication or division operation is done on a
rational number with an irrational number, the result is an
irrational number.
• When two irrational numbers are added, subtracted, multiplied or
divided, the result may be a rational or an irrational number.
7. HIGHEST COMMON FACTOR (HCF)
• The HCF (Highest Common Factor) of two
numbers is the highest number among all the
common factors of the given numbers. For
example, HCF of 12 and 36 is 12 because 12 is
the highest common factor of 12 and 36.
8. LEAST COMMON MULTIPLE ( L.C.M )
* The least common multiple (L.C.M) of two or more number is the
smallest number which can be exactly divided by each of the given
number
Let us find the LCM of 28 and 12
Multiples of 28 are 28 , 56 , 84 , 112 ………
Multiples of 12 are 12 , 24 , 36 , 48 , 60 , 72 , 84 , 96 ……….
The least common multiple (L.C.M) of 28 and 12 is 84
