  In the present paper we explore a way to represent numbers with respect to
the base $-\frac32$ using the set of digits $\{0,1,2\}$. Although this number
system shares several properties with the classical decimal system, it shows
remarkable differences and reveals interesting new features. For instance, it
is related to the field of $2$-adic numbers, and to some ``fractal'' set that
gives rise to a tiling of a non-Euclidean space.
