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, ), ppb (parts-per-billion, ), ppt (parts-per-trillion, ) and ppq (parts-per-quadrillion, ).