Definition:
An rational number is a number that can be expressed as the quotient or fraction p/q of two integers, where q is not equal to zero. An irrational number is a number that cannot be expressed as a simple fraction or ratio of two integers.

Difference:

Rational numbers can be expressed as fractions, while irrational numbers cannot be expressed as fractions. Rational numbers have a terminating or repeating decimal representation, while irrational numbers have non-terminating and non-repeating decimal representation.

Representation:
The reason why rational numbers are represented in the form of p/q is to show that they are a quotient or fraction of two integers. This form helps in understanding the relationship between the numerator and denominator. It also helps in performing arithmetic operations on rational numbers easily by following the rules of fractions.

Use of p/q form:
1. Clarity: Representing rational numbers in the form of p/q provides clarity about the relationship between the numerator and denominator.
2. Arithmetic operations: Using the p/q form makes it easier to perform arithmetic operations like addition, subtraction, multiplication, and division on rational numbers.
3. Comparisons: It allows for easy comparison of rational numbers by comparing their numerators and denominators.
4. Standard representation: The p/q form is a standard and consistent way to represent rational numbers, making it easier for communication and mathematical calculations.
In conclusion, representing rational numbers in the form of p/q helps in understanding their nature as fractions and facilitates mathematical operations and comparisons. It is a standard representation method that aids in clarity and consistency in mathematical expressions and calculations.