The term “dex” comes up rather frequently in astronomy discussions but is rarely defined in textbooks. The idea of a dex is straightforward—a dex is simply an order of magnitude. More formally, a difference of $$x$$ dex is a change by a factor of $$10^x$$. (Although the dex is almost always used in relation to some other quantity, it can in principle be used to represent a unitless number. Thus the number $$x$$ can be written $$10^x$$ dex.)

We use the terms “order of magnitude” and “factor of $$x$$” all the time, though, so why use the term dex? The reason is that it comes in handy when talking about fractions of an order of magnitude. It’s particularly useful when talking about metallicity. Metallicity is measured logarithmically relative to the abundance of metals in the Sun, and accordingly it must be unitless.

As an example, let’s take a look at Fischer & Valenti (2005). In this paper the authors present a correlation between the metallicity of stars and the probability that the star hosts a planet—stars with higher metallicities are more likely to host a planet. This result is shown in figure 5:

We can see that the sample of stars spans a range of [Fe/H] from -0.5 to 0.5, which is one order of magnitude, or one dex. Although it was just as easy to say order of magnitude as it was to say dex in that case, suppose we asked how wide the bins in this histogram were. There are ten bins spanning an order of magnitude, so the width of each bin is a factor of $$10^{0.1} \approx 1.26$$. This is clumsy, so instead we simply say that each bin has a width of 0.1 dex.