trillionth

Trillionth is the fractional quantity that equals one divided by a trillion. In numeric terms it is 1/1,000,000,000,000, or 1×10−12. In decimal form this is 0.000000000001. The term is used to describe extremely small portions or probabilities, as well as tiny scales in science and engineering.

Scale context is important. In the short-scale system common in modern English-speaking countries, a trillion is 10^12, so a trillionth is 10−12. Some historical or regional usages employed a long scale, where a trillion meant 10^18; in that case a trillionth would be 10−18. Although long-scale usage persists in limited contexts, the short scale is now standard in most scientific and international references.

Common examples of trillionths appear in measurements and quantities. A trillionth of a meter is a picometer, and a trillionth of a second is a picosecond. A trillionth of a liter is a picoliter, and a trillionth of a gram is a picogram. In statistics and physics, quantities on the order of 10−12 are described as being in the parts-per-trillion range, reflecting an extremely small proportion.

Etymology-wise, the word trillionth is formed from trillion plus the ordinal suffix -th. The root trillion traces to historical terms for very large numbers, with usage that has varied across scales and languages.