  The Tarski number of a non amenable group is the smallest number of pieces
needed for a paradoxical decomposition of the group. Non amenable groups of
piecewise projective homeomorphisms were introduced by Monod, and non amenable
finitely presented groups of piecewise projective homeomorphisms were
introduced by the author in joint work with Justin Moore. These groups do not
contain non abelian free subgroups. In this article we prove that the Tarski
number of all groups in both families is at most 25. In particular we
demonstrate the existence of a paradoxical decomposition with 25 pieces.
  Our argument also applies to any group of piecewise projective homeomorphisms
that contains as a subgroup the group of piecewise $PSL_2(\mathbb{Z})$
homeomorphisms of $\mathbb{R}$ with rational breakpoints, and an affine map
that is a not an integer translation.
