How do you calculate percent error, and what does it tell you about a measurement?

How do you calculate percent error, and what does it tell you about a measurement?

• A. Percent error = (experimental − true) / true × 100%; assesses bias direction only.
• B. Percent error = (experimental − true) / true; expressed as a decimal rather than percent.
• C. Percent error = |experimental − true| / true × 100%; assesses accuracy relative to a known standard.
• D. Percent error = |true − experimental| × 100%; overstates the difference.

Answer: (C)

Percent error tells you how far a measurement is from the accepted true value, expressed as a percentage of that true value. It’s calculated using the absolute value of the difference between the measured value and the true value, divided by the true value, and then multiplied by 100%. The absolute value is key because you want the size of the discrepancy, not its direction, so the result stays a nonnegative measure of accuracy. This form directly shows how close your measurement is to the standard: a small percent error means good agreement with the true value, while a large percent error indicates a larger deviation. That’s why the correct approach uses the absolute difference divided by the true value and then converts to percent. Other options miss one or more parts: leaving out the absolute value gives a signed error that can complicate interpretation of accuracy; omitting division by the true value ignores the relative size of the error; or expressing the result as a decimal rather than a percent does not put the error in the common percent format.

Percent error tells you how far a measurement is from the accepted true value, expressed as a percentage of that true value. It’s calculated using the absolute value of the difference between the measured value and the true value, divided by the true value, and then multiplied by 100%. The absolute value is key because you want the size of the discrepancy, not its direction, so the result stays a nonnegative measure of accuracy.

This form directly shows how close your measurement is to the standard: a small percent error means good agreement with the true value, while a large percent error indicates a larger deviation. That’s why the correct approach uses the absolute difference divided by the true value and then converts to percent.

Other options miss one or more parts: leaving out the absolute value gives a signed error that can complicate interpretation of accuracy; omitting division by the true value ignores the relative size of the error; or expressing the result as a decimal rather than a percent does not put the error in the common percent format.