1. What is Numerical Error?

Numerical error refers to the difference between an approximate value and the exact or true value. It quantifies the accuracy of numerical computations and measurements in scientific and engineering applications.

2. How Does the Calculator Work?

The calculator uses the relative error formula:

Where:

• \( \text{Approximate} \) — The measured or calculated value
• \( \text{Exact} \) — The true or reference value
• \( | \cdot | \) — Absolute value function

Explanation: This formula calculates the percentage error by comparing the absolute difference between approximate and exact values relative to the exact value.

3. Importance of Error Calculation

Details: Calculating numerical error is essential for assessing the reliability of measurements, validating computational methods, and ensuring quality control in scientific research and engineering applications.

4. Using the Calculator

Tips: Enter both approximate and exact values. The exact value cannot be zero (division by zero error). Values can be positive or negative, but the error is always expressed as a positive percentage.

5. Frequently Asked Questions (FAQ)

Q1: What is the difference between absolute and relative error?
A: Absolute error is the simple difference between approximate and exact values, while relative error expresses this difference as a percentage of the exact value.

Q2: When is numerical error calculation most important?
A: It's crucial in scientific experiments, engineering measurements, computational simulations, and any situation where accuracy and precision matter.

Q3: What is an acceptable error percentage?
A: Acceptable error varies by field. In some applications, 1% error may be acceptable, while in others, even 0.1% may be too high.

Q4: Can this calculator handle negative values?
A: Yes, the calculator uses absolute values in the denominator, so it can handle both positive and negative inputs.

Q5: Why can't the exact value be zero?
A: Division by zero is mathematically undefined, so the exact value must be non-zero for the calculation to work.