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Absolute Value

Concept

Absolute value

The absolute value of a number is the distance between the number and 00 on the number line. For example, the absolute value of 3,3, expressed as 3,|3|, is 3.3.

A number line which shows the absolute value of -3 and 3

The absolute value applies to negative numbers as well. The absolute value of -3\text{-}3 is the distance from -3\text{-} 3 to 00 on the number line.

A number line which shows the absolute value of -3 and 3

The absolute value of 33 and -3\text{-}3 are equal, 3=-3=3. |3|=|\text{-}3|=3. Therefore, the absolute value is the positive value of a number. Hence, the definition of the absolute value of aa is divided into two cases: the first where aa is positive or 00, and the second when aa is negative. a={a,a0-a,a<0 |a|=\begin{cases}a,\quad a\geq 0 \\ \text{-} a,\quad a<0 \end{cases}

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