summary:Let L(θ,λ) be the set of limit points of the fractional parts {λθn}, n=0,1,2,…, where θ is a Pisot number and λ∈Q(θ). Using a description of L(θ,λ), due to Dubickas, we show that there is a sequence (λn)n≥0 of elements of Q(θ) such that Card(L(θ,λn))<Card(L(θ,λn+1)), ∀n≥0. Also, we prove that the fractional parts of Pisot numbers, with a fixed degree greater than 1, are dense in the unit interval