Skill: Interpret absolute value as distance from zero

Absolute value tells how far a number is from $0$ on the number line. Distance is never negative, so an absolute value is always $0$ or positive.

For example, find $\vert -3 \vert$.

1. Locate $-3$ on the number line.
2. Count the spaces from $-3$ to $0$: there are $3$ spaces.
3. Distance does not depend on direction, so the distance is positive.

Therefore,

$$\vert -3 \vert =3$$

The number $3$ is also $3$ spaces from $0$, so $\vert 3 \vert =3$. This shows that opposite numbers have the same absolute value. Also, $\vert 0 \vert =0$ because $0$ is no distance from itself.