Question. Evaluate the expression |-31.889|
Explanation:
The absolute value of a number represents its distance from zero on the number line, always as a non-negative value.
Definition of Absolute Value:
For any real number a:
- If a is positive or zero, then |a| = a.
- If a is negative, then |a| = -a (removing the negative sign).
Applying the Definition:
Given |−31.889|:
- The number inside the absolute value bars is −31.889.
- Since it is negative, we take its positive counterpart: ∣−31.889∣=31.889|−31.889| = 31.889
Visual Representation:
Imagine a number line:
…−33−32−31.889−31−30…… -33 \quad -32 \quad -31.889 \quad -31 \quad -30 …- The point −31.889 is 31.889 units away from 0.
- Absolute value removes direction and considers only the magnitude.
Real-World Application:
Absolute values are crucial in various fields:
- Finance: Calculating net losses or gains.
- Physics: Measuring distances irrespective of direction.
- Engineering: Ensuring correct calculations in structures and circuits.
Thus, the absolute value of −31.889 is 31.889, as it represents the distance from zero, ignoring direction.
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