This paper focuses on the representation of a proper fraction "a"/"b" by a decimal number base "n" where "n" is any integer greater than 1. The scope is narrowed to look at only fractions where "a","b" are positive integers with "a" less than "b" and "b" not equal to 0 nor equal to 1. Some relationships were found between "b" and "n", which determine whether the representation will become either finite decimal, pure recurring decimal or mixed decimal base "n". Three theorems have been proven to indicate the deciding factors and the relationships. In addition, the length of the finite decimal numbers base "n" was further explored.