Activated dissipative conductivity σ xx = σ* xx exp(−Δ/T) and the activated deviation of the Hall conductivity from the precise quantization δσ xy = σ xy −ie 2 /h= σ* xy exp(−Δ/T) are studied in a plateau range of the quantum Hall effect. The prefactors σ* xx and σ* xy are calculated for the case of a long-range random potential in the framework of a classical theory. There is a range of temperatures T 1 ≪ T ≪ T 2 where σ* xy = e 2 /h. In this range σ* xy ≈ (e 2 /h)(T/T 2 ) 80/21 ≪ σ* xx . At large T ≫ T 2 , on the other hand, σ* xy = e 2 /h and σ* xx = (e 2 h)(T 2 T) 10/13 ≪ σ* xy . Similar results are valid for a fractional plateau near the filling factor p/q if charge e is replaced by e/q.