Quantized conductance behavior of gold nanowires was studied under electrochemical potential control. We fabricated 1-nm-long monoatomic wires in solution at room temperature. Electrochemical potential significantly affected the stability of the monoatomic wire and fractional conductance peak occurrence in the conductance histogram. We revealed that the hydrogen adsorption on gold monoatomic wires was a decisive factor of the fractional peak, which was originated from the dynamic structural transition between two bistable states of the monoatomic wire showing the unit and the fractional values of the conductance. We could tune the stability of these bistable states to make the fractional conductance state preferable.