Q stands for quotient. The letter R was already used for the set of Real numbers.
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In number systems Rational number is not represented just by q . they are represented in the form of p and q . P/q is rational number where q is not equal to zero.
The set of rational numbers is represented by Q.
A rational number is any number of the form p/q where p and q are integers and q is not zero. If p and q are co=prime, then p/q will be rational but will not be an integer.
A rational number can be expressed as a ratio in the form, p/q, where p and q are integers and q > 0.
A rational number is one that can be expressed as a ratio of two integers. That is, a number x is rational if and only if it is equivalent to p/q for some integers p and q where q is not 0.