Division No non-integer rational number can be represented as a finite base-φ number. In other words, all finitely representable base-φ numbers are either integers or (more likely) an irrational in a quadratic field Q[]. Due to long division having only a finite number of possible remainders, a division of two integers (or other numbers with finite base-φ representation) will have a recurring expansion, as demonstrated above.
Division No non-integer rational number can be represented as a finite base-φ number In other words, all finitely representable base-φ numbers are either integers or (more likely) an irrational in a quadratic field Q[]. Due to long division having only a finite number of possible remainders a division of two integers (or other numbers with finite base-φ representation) will have a recurring expansion as demonstrated above.