order of magnitude

An order of magnitude is an exponential change of plus-or-minus 1 in the value of a quantity or unit. The term is generally used in conjunction with power-of-10 scientific notation.

In base 10, the most common numeration scheme worldwide, an increase of one order of magnitude is the same as multiplying a quantity by 10. An increase of two orders of magnitude is the equivalent of multiplying by 100, or 10². In general, an increase of n orders of magnitude is the equivalent of multiplying a quantity by 10ⁿ. Thus, 2315 is one order of magnitude larger than 231.5, which in turn is is one order of magnitude larger than 23.15.

As values get smaller, a decrease of one order of magnitude is the same as multiplying a quantity by 0.1. A decrease of two orders of magnitude is the equivalent of multiplying by 0.01, or 10^-2. In general, a decrease of n orders of magnitude is the equivalent of multiplying a quantity by 10^-n. Thus, 23.15 is one order of magnitude smaller than 231.5, which in turn is one order of magnitude smaller than 2315.

In the Standard International (SI) System of Units, most quantities can be expressed in multiple or fractional terms according to the order of magnitude. For example, attaching the prefix "kilo-" to a unit increases the size of the unit by three orders of magnitude, or one thousand (10³). Attaching the prefix "micro-" to a unit decreases the size of the unit by six orders of magnitude, the equivalent of multiplying it by one millionth (10^-6). Scientists and engineers have designated prefix multipliers from septillionths (10^-24) to septillions (10²⁴), a span of 48 orders of magnitude.

Also see prefix multipliers, scientific notation, significant figures, and Standard International (SI) System of Units.