We can compare two numbers by looking at their positions on the number line: The number farther to the right is greater. The number farther to the left is less.

Sometimes we want to compare which one is closer to or farther from 0. For example, we may want to know how far away the temperature is from the freezing point of $0 ^\circ \text{C}$, regardless of whether it is above or below freezing. 

The absolute value of a number tells us its distance from 0.

For example, the absolute value of -4 is 4, because -4 is 4 units to the left of 0. The absolute value of 4 is also 4, because 4 is 4 units to the right of 0. Opposites always have the same absolute value because they are both the same distance from 0.

The distance from 0 to itself is 0, so the absolute value of 0 is 0. Zero is the only number whose distance to 0 is 0. For all other absolute values, there are always two numbers—one positive and one negative—that have that distance from 0.

To say, “the absolute value of 4,” we write "$|4|$."

To say, “the absolute value of -8 is 8,” we write "$|\text-8|=8$."