In this article we study a numeration system previously used to prove combinatorial properties in discrete geometry: the \(\Delta \) -numeration. Since this system, introduced via the fully subtractive algorithm, has been seen mainly as a tool, we propose here to study it from the point of view of numeration systems. In particular, we make the link with \(\beta \) -numeration and Cantor real bases. We reintroduce the rewriting system introduced to calculate in \(\Delta \) -numeration. This systems is based on the properties of the fully subtractive algorithm and is normalising. Finally, we study the ultimately periodic case, a special case of alternate bases, and show that the ultimately periodic words represent exactly the elements of \(\mathbb {Q}[\beta]\) where \(\beta \) is the inverse of a Pisot number.