667. Find the distance between points $A$ (with coordinate $a$) and $B$ (with coordinate $b$).
$\triangle$ To find this distance, one needs to subtract the smaller coordinate from the larger one. Thus, it equals $b-a$ when $b>a$ and $a-b$ when $a>b$. Naturally, the distance is zero when $a=b$. $\triangleleft$

The formula for the distance is conveniently written using the modulus sign:

The absolute value, or modulus of a number $u$ is the number itself if $u$ is non-negative, and the opposite number $-u$ if $u$ is negative. Notation: $|u|$. Thus,

$$
|u|=\left\{\begin{array}{l}
u, \text { if } u \geqslant 0 \\
-u, \text { if } u<0
\end{array}\right.
$$

For example, $|3|=3,|0|=0,|-2|=|2|=2$.

Often, when asked "What is the modulus of a number?", schoolchildren answer: "It's the number without a sign." Although they are rightly scolded for such an answer (since it is not a definition but something unknown), it serves as a practical recipe for finding the modulus if the number is given in the form of a decimal or common fraction. However, one must be careful: