Billionth

One billionth is the reciprocal of a billion, which means it has one of two definitions depending on whether the long scale or short scale definition is being used.

Short scale

In the short (or American) scale, a billionth is equal to 0.000 000 001, or 1 x 10⁻⁹ in scientific notation. The prefix for this number is nano, and is abbreviated as "n" (for example, in electronics, one nanofarad would be written as 1 nF).

Long scale

In the long (or English) scale, a billionth is equal to 0.000 000 000 001, or 1 x 10⁻¹² in scientific notation. The prefix for this number is pico-, and is abbreviated as "p" (for example, in electronics, one picofarad would be written as 1 pF).

References

Parts-per notation

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).

Overview

Parts-per notation is often used describing dilute solutions in chemistry, for instance, the relative abundance of dissolved minerals or pollutants in water. The unit “1 ppm” can be used for a mass fraction if a water-borne pollutant is present at one-millionth of a gram per gram of sample solution. When working with aqueous solutions, it is common to assume that the density of water is 1.00 g/mL. Therefore, it is common to equate 1 gram of water with 1 mL of water. Consequently, 1 ppm corresponds to 1 mg/L and ppb corresponds to 1 μg/L.