About Real Numbers

REAL NUMBERS-
Real numbers are simply the combination of Rational and Irrational numbers in the number system.
A real number is any positive or negative number.


Real numbers that include decimal points are also called floating point numbers, since the decimal "floats" between the digits.


 (i)Rational Numbers:-
Can be expressed as the quotient of two integers (i.e, fraction ) in p/q form where p is numerator and q is denominator,such that denominator is not zero.rational number can be integers, repeating decimal etc.
IMP:-
every fraction is not a rational number because fractions can contain irrational number such as. 2/√3 or √5/8. So all fractions are not rational number and every rational number is not fraction.


                                      (ii)Irrational Numbers:-
Can not be expressed as the quotient of two integers (i.e, a fraction) such that the denominator is not zero, 
                                         or
An irrational number is a number that cannot be expressed as a fraction p/q  for any integers p and q. Irrational numbers have decimal expansions that neither terminate nor become periodic.
                                       or
A real number that can NOT be made by dividing two integers (an integer has no fractional part).

"Irrational" means "no ratio", 












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