What is the definition of Partial Pressure?

The partial pressure of a certain gas or vapor is the pressure which that gas
or vapor would exert if it alone were present in the vessel.

Important note: Particularly in rough vacuum technology, the total pressure
of a mix of gases and vapors is often understood to be the sum of the partial
pressures of all the gases present in the mix – in the case of the specifications of  “partial ultimate pressure” and "total ultimate pressure" in relation to  a rotary vane pump, for example.