1. What is Absolute Value?

The absolute value of a number is its distance from zero on the number line, without considering direction. For any rational number x, the absolute value is defined as:

2. How Does This Calculator Work?

The calculator:

1. Takes a list of rational numbers (comma separated)
2. Calculates the absolute value of each number
3. Sorts the original numbers by their absolute values from least to greatest
4. Displays both the sorted original numbers and their absolute values

3. Importance of Absolute Value

Details: Absolute value is fundamental in mathematics for measuring magnitude regardless of direction. It's used in distance calculations, error measurements, and many real-world applications where only the size of a quantity matters, not its sign.

4. Using the Calculator

Tips: Enter numbers separated by commas (e.g., "3, -1.5, 0, -4.2"). The calculator will ignore any non-numeric values and sort the valid numbers by their absolute values.

5. Frequently Asked Questions (FAQ)

Q1: What's the difference between absolute value and regular value?
A: Absolute value removes the sign, giving only the magnitude. For example, |-5| = 5 and |3| = 3.

Q2: How are numbers with equal absolute values sorted?
A: Numbers with the same absolute value (like 5 and -5) will appear in the order they were entered.

Q3: Can I enter fractions or decimals?
A: Yes, the calculator accepts any rational numbers in decimal form (e.g., 0.5, -3/4 as -0.75).

Q4: What happens if I enter non-numeric values?
A: Non-numeric entries will be ignored in the calculation.

Q5: Why sort by absolute value?
A: This helps identify numbers with smallest magnitudes first, useful in error analysis and certain statistical applications.