Integers with absolute values refer to the distance of an integer from zero on the number line, irrespective of its sign. In other words, the absolute value of an integer is its non-negative value.
Understanding Absolute Value
The absolute value represents the magnitude of a number. It answers the question, "How far is this number from zero?" Since distance is always non-negative, absolute values are always zero or positive.
Examples
- The absolute value of -5 is 5 because -5 is 5 units away from zero (Reference: 2:19-10:34).
- The absolute value of 5 is 5 because 5 is 5 units away from zero.
- The absolute value of 0 is 0 because 0 is 0 units away from zero.
Notation
We denote the absolute value of a number x using vertical bars: |x|.
- | -5 | = 5
- | 5 | = 5
- | 0 | = 0
Practical Insights
- Absolute values are useful in various mathematical and real-world contexts where only the magnitude of a quantity matters.
- For example, when calculating the difference between two temperatures, the absolute value ensures the result is positive, representing the magnitude of the temperature difference.
Absolute Value in Equations
When solving equations involving absolute values, it's crucial to consider both positive and negative possibilities of the expression inside the absolute value.
For example, if |x| = 3, then x can be either 3 or -3.
