I'm currently unaware of terminology or notation that refers to "some function" of a rational number similarly to how "absolute value" relates to a number. Let me explain.
If one wants to state that a number $x$ must be between $-a$ and $a$ (for some positive value $a$), one can state that $-a < x < a$. This can also be stated as $|x| < a$, or "the absolute value of $x$ must be less than $a$."
If one wants to state that a number $x$ must be between $\frac{1}{a}$ and $a$, one can state that $\frac{1}{a} < x < a$. How can this also be stated in a more compact way, similar to the notation/terminology for the absolute value of a number? Something like $f(x) < a$, or "the magic ratio function of $x$ must be less than $a$."
(As an additional thought, similarly to how the absolute value can be considered the "distance from zero", this unknown function I am trying to find could be considered the "scaling factor from 1.")
If $x$ is between $a$ and $b$, then
$a<x<b \implies \frac{a+b}{2}-\frac{b-a}{2}<x<\frac{a+b}{2}+\frac{b-a}{2}$ $\implies -\frac{b-a}{2}<x-\frac{a+b}{2}<\frac{b-a}{2}$
Therefore $$\bigg|x-\frac{a+b}{2}\bigg|<\frac{b-a}{2}$$