Abstract

A "general" continued fraction representation of a real number x is one of the form 〖x= a〗_0 + b_1/(a_1+b_2/(a_2+b_3)/(a_3+⋯………@ + b_n/a_N ))) Where a_0 〖 ,a〗_1, . ... and b_1, b_2…..are integers. In this article we define convergents of a finite continued fraction and continued fractions with positive quotients and discuss fraction algorithm and Euclid’s algorithm