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This paper contains an algebraic constructive and self-contained account ofthe invariance rule of the digital root under division for an arbitrary naturalbasis representation. Both the cases of repeating and non-repeating fractionalsare treated. In the preliminary section some known results such as theuniqueness in the representation of a fraction are discussed for both thefinite and infinite bases cases. Simple examples are introduced throughout thetext for illustrative purposes.

Properties of the Digital Root and its Extension to Rational Numbers -- an Algebraic Approach