Interpret absolute value as distance from zero

Absolute value is the nonnegative distance between a number and zero on the number line: $|a|$ measures how far an integer or rational number $a$ lies from 0, regardless of direction. Thus, opposite numbers have equal absolute values, while 0 has absolute value 0; this interpretation supports comparing magnitudes and reasoning about signed quantities, without extending to advanced absolute-value functions or abstract generalizations.

Detailed Explanation: 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 $\vert -3 \vert$ .

Locate $-3$ on the number line.
Count the spaces from $-3$ to $0$ : there are $3$ spaces.
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.

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Order of Operations - Real Numbers, Absolute Value, Radicals and Exponents

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Interpret absolute value as distance from zero

Detailed Explanation: Interpret absolute value as distance from zero

Learn by doing: Interpret absolute value as distance from zero

Practice with unlimited practice problems

Practice:

Order of Operations - Real Numbers, Absolute Value, Radicals and Exponents