There are a number of ways to define the concentration of a gas in a mixture beyond the partial pressure. These are typically given in terms of the ratios of the number of particles or number of moles like mole fraction or mole percent. For very small concentrations, we tend to use measures like parts per million (ppm) or parts per billion (ppb).
Be aware that ppm (and ppb) are defined differently for gas mixtures than liquid mixtures. For a gas mixture ppm refers to the number of gas particles (atoms, molecules, or moles) of a particular type that exists in the mixture per 1,000,000 total gas particles. In liquid mixtures, ppm is based on the mass of the solute per overall mass of solution.