The ratio of output power to input power is interpreted differently depending on the context. The ratio is referred to as gain when referring to amplifiers, and when referring to machines, it is known as efficiency.
Amplifier gain does not have any unit because it is a ratio of the same unit signals. However, when the gain is represented in the logarithmic scale, it has a unit. The unit is the decibel, which is a one-tenth fraction of bel. The decibel notation is also used to express the amplitude of various signal parameters, such as voltage and current, relative to a given reference level.