 Despite using an irrational number base, when using standard form, all non-negative integers have a unique representation as a terminating (finite) base-φ expansion.The set of numbers which possess a finite base-φ representation is the ring Z[]; it plays the same role in this numeral systems as dyadic rationals play in binary numbers, providing a possibility to multiply.Other numbers have standard representations in base-φ, with rational numbers having recurring representations.