A rational number is defined as a fraction with an Integer numerator and a non-zero natural number denominator which is given p / q, where p is any integer and q is any non-zero natural number. We define the Fractions by p / q = r / s if and only if p · q = r · s. The Set of Rational Numbers are denoted by Q. There are two types of rational number that are proper fraction rational number and improper fraction rational number. The proper fraction rational numbers are those numbers which can be divided or factorized easily for example 16/32=1/2 ,2/4=1/2 or 15/60=1/4 etc. On other hand the improper fraction rational numbers are those numbers which cannot be divided or factorized easily for example 13/22,5/13,16/33 etc. So these are the basic types of rational numbers. Two different fractions may correspond to the same rational number for example 1⁄3 and 3⁄6 are equal, that is: 3/6=1/3.
The absolute value of p is greater than q, so that the absolute value of the fraction is greater than 1. Fractions of rational number can be greater than, less than or equal to 1 and can also be positive, negative, or zero and every integer can be written as a fraction with denominator 1. For example −5 can be written −5⁄1. The real number which is not rational is called irrational. Irrational numbers are √2, π, and e. In the Irrational Numbers the decimal numbers values are not repeated for example the value of pi is 3.1423453291……… in this value no values are repeating continuously. So that the irrational number is one which cannot be expressed as simple fraction is known as irrational number. The each and every real number has rational numbers and the rationales numbers are subset of the Real Numbers.