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Calculate the percent error between experimental and theoretical values. Essential for scientific measurements, lab reports, and data analysis.
Formula: |Experimental - Theoretical| / |Theoretical| × 100
Example: Measured 9.5, Expected 10 = |9.5-10|/10 × 100 = 5%
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Percent error measures the accuracy of an experimental measurement by comparing it to the accepted or theoretical value. It's calculated as: |Experimental - Theoretical| / |Theoretical| × 100%. Lower percent error indicates higher accuracy.
We use absolute value because percent error measures the magnitude of error, not its direction. Whether you measured too high or too low, you want to know how far off you were. The absolute value ensures the error is always positive.
Generally, <5% is excellent, 5-10% is good, and 10-20% is acceptable depending on the context. For precise scientific work, aim for <5%. Some fields or experiments may have different standards based on their precision requirements.
No, percent error is always positive because we use the absolute value of the difference. If you need to know whether you measured too high or too low, use signed error or percentage change instead.
Common sources include: measurement uncertainty, equipment limitations, human error, environmental conditions, and systematic errors in the experimental setup. Understanding these helps improve future measurements.
To reduce error: use more precise equipment, calibrate instruments, take multiple measurements and average them, control environmental factors, improve technique, and identify/eliminate systematic errors.
Percent error compares an experimental value to a known theoretical value: |Exp-Theo|/Theo × 100. Percent difference compares two measured values symmetrically: |V1-V2|/avg × 100. Use error when you have a 'correct' value.
If they're exactly equal, the percent error is 0%. This represents perfect accuracy, though in practice, small measurement uncertainties usually result in some non-zero error.
Percent error is a fundamental concept in scientific measurement that quantifies the accuracy of experimental results. It expresses the magnitude of error as a percentage of the accepted or theoretical value, making it easy to compare measurements across different scales and units.