1. What is Fractional Uncertainty?

Fractional uncertainty is a measure of the uncertainty in a measurement relative to the size of the measurement itself. It provides a dimensionless quantity that expresses the precision of a measurement.

2. How Does the Calculator Work?

The calculator uses the fractional uncertainty formula:

Where:

• Error — The absolute uncertainty or error in the measurement
• Value — The measured value or quantity

Explanation: The fractional uncertainty represents the ratio of the measurement error to the actual measured value, providing a relative measure of uncertainty.

3. Importance of Fractional Uncertainty

Details: Fractional uncertainty is crucial in scientific measurements as it allows for comparison of precision across different measurements and scales. It helps determine the reliability of experimental results and is essential in error propagation calculations.

4. Using the Calculator

Tips: Enter the error (absolute uncertainty) and the measured value. Both values must be positive numbers, and the value cannot be zero. The calculator will compute the fractional uncertainty as a dimensionless quantity.

5. Frequently Asked Questions (FAQ)

Q1: What is the difference between absolute and fractional uncertainty?
A: Absolute uncertainty is the actual error in the measurement (with units), while fractional uncertainty is the ratio of error to value (dimensionless).

Q2: How is fractional uncertainty related to percentage uncertainty?
A: Percentage uncertainty is simply fractional uncertainty multiplied by 100%. For example, a fractional uncertainty of 0.05 equals 5% uncertainty.

Q3: When should I use fractional uncertainty?
A: Use fractional uncertainty when comparing the precision of measurements with different magnitudes or when propagating errors through calculations.

Q4: Can fractional uncertainty be greater than 1?
A: Yes, though it indicates very high uncertainty relative to the measured value, which may suggest problematic measurements.

Q5: How does fractional uncertainty affect significant figures?
A: The fractional uncertainty determines how many significant figures are meaningful in a measurement. Smaller fractional uncertainty allows for more significant figures.