1/f noise in semiconductor devices and circuits provides important information regarding quality of the interface as well as the transport mechanism. In 1D and 2D channel materials, 1/f noise also provides information on stability under ambient conditions, including effects of contaminants adsorbed on the surface. In addition, noise levels are important in evaluating suitability of the device for analog and digital applications. In this work, we have fabricated back-gated field-effect transistors (FETs) using various thicknesses of mechanically exfoliated MoS2 flakes (bilayer and 15 layer flakes) and studied the 1/f noise under ambient conditions. The on-current of the devices scales with the number of layers. The Hooge parameters inferred from the measured noise amplitudes and calculated carrier densities are comparable to prior reports on devices such as CNTs and graphene FETs, even when measured under ambient conditions. The effect of channel and contacts on both the conductance and noise can be inferred from bias-dependent current and noise measurements.