dex

The term dex (for decimal exponent) was coined within astrophysics as a convenient unit indicating any number or ratio's order-of-magnitude, i.e., its (rounded) base-10 logarithm. For example, 100 could be described as 2 dex, or two numbers that differ by a factor of 1000 could be said to differ by 3 dex. (The phrase, order-of-magnitude is used slightly differently: differing by 3 orders of magnitude is synonymous with differing by 3 dex, but indicating a number to be close to 100 would often be stated as having an order-of-magnitude of ten to the two). As such a unit, a dex is sometimes cited with fractions (making it the value's more-precise log base 10) whereas a cited order-of-magnitude is commonly rounded to an integer. The term dex is used in astrophysics but order-of-magnitude may well be more common.

The term decimal exponent describes the exponent in the typical scientific notation of numbers:

2.40×107
 aka
2.40e7

This number's decimal exponent is 7 and the number could be roughly described as "7 dex" or "having an order-of-magnitude of 10 to the 7". It could also be described as "7.38 dex", which is the number's log base 10 not rounded to an integer. Example of a ratio as a dex: "Jupiter's and Earth's masses differ by 2.5 dex" (i.e., log₁₀ of 318, their ratio). This statement is a short way of saying "the base-10 logs of Jupiter's and Earth's masses differ by 2.5".