is "commensurability" as simple as saying a and b are rational? I am trying to better understand commensurability. Wikipedia says: 

two non-zero real numbers a and b are said to be commensurable if
  $\frac{a}{b}$ is a rational number.

Richard Courant in Introduction to Calculus and Analysis says:

Two quantities whose ratio is a rational number are called commensurable
  because they can be expressed as integral multiples of a common
  unit.

First of all, can't we just "cheat" and say that the common unit is $1$? I'm not even sure if that's cheating or if that's what he actually means.
Furthermore, looking at the Wikipedia definition, since a "rational number" means that $a$ and $b$ must be integers, shouldn't the beginning of that sentence actually read, "two non-zero integers" (and maybe $a$ can also be $0$)? Or are there additional cases we want to allow to be commensurable?
Bottom line, I'm not sure what commensurability means other than "both numbers must be rational numbers," if that is indeed what it means.
For context, I'm reading this in the context of Courant demonstrating that irrational numbers exist. He's doing this by showing that some numbers exist which are not rational fractions (e.g. $\sqrt{2}$), but he equates that with being "incommensurable with the unit length":

$x$ and $y$ are commensurable if there exists a real number, $r$ and positive integers $m$ and $n$ such that $x = mr$ and $y=nr$. If such an $r$ exists, it is called a common measure. If $x$ and $y$ are commensurable, we can aviod mention of a common measure by writing $x : y :: m : n$, or $\dfrac xy = \dfrac mn$. The value of $r$ depends on the values of $x$ and $y$. Saying, for example, that $\sqrt 2$ is irrational is equivalent to saying that $\sqrt 2$ and $1$ are incommensurable.
