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In science and engineering, the parts-per notation is a set of pseudo-units to describe small values of miscellaneous dimensionless quantities, e.g. mole fraction or mass fraction. Since these fractions are quantity-per-quantity measures, they are pure numbers with no associated units of measurement. Commonly used are ppm (parts-per-million, 10−6), ppb (parts-per-billion, 10−9), ppt (parts-per-trillion, 10−12) and ppq (parts-per-quadrillion, 10−15).