The best approximation is defined as: The rational number p/q is the best approximation to a real number x if the distance from p/q to x on the real line is less than the distance from any other rational number(with denominator less than or equal to q) to x.
alternatively, a fraction p/q is a best approximation of the second kind to a real number t if for every fraction a/b with denominator less than or equal to q, we have |qt – p| <|bt – a|.