Thanks for commenting,with respect I want to ask you the exact definition of rational number.
The site says, "Rational numbers are those numbers which can be represented in the form of p/q where p and q are REAL numbers and q cannot be zero."
The rational numbers are those numbers that can be represented as the ratio of two INTEGERS in lowest terms, i.e. no common factors.
http://mathworld.wolfram.com/RationalNumber.htmlhas a definition that says it's the ratio of integers (and not reals). I think the statement that q ≠ 0 is redundant, since no number is defined that way anyway. The phrase where p and q are in lowest terms is missing from their definition and I think that's a mistake, as the proof that sqrt(2), for example, is irrational relies on that property.