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Nathaniel measured a line to be 12.2 inches long. If the actual length of the line is 10.2 inches, then what was the percent error of the measurement, to the nearest tenth of a percent?
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Nathaniel measured a line to be 1212.22 inches long. If the actual length of the line is 1010.22 inches, then what was the percent error of the measurement, to the nearest tenth of a percent?\newlineAnswer:______ % \%

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Q. Nathaniel measured a line to be 1212.22 inches long. If the actual length of the line is 1010.22 inches, then what was the percent error of the measurement, to the nearest tenth of a percent?\newlineAnswer:______ % \%
  1. Understand Percent Error: Understand the concept of percent error. Percent error is a measure of how inaccurate a measurement is, represented as a percentage of the actual value. The formula for percent error is: Percent Error = (Measured ValueActual Value/Actual Value)×100%(|\text{Measured Value} - \text{Actual Value}| / \text{Actual Value}) \times 100\%
  2. Identify Values: Identify the measured value and the actual value from the problem.\newlineMeasured Value = 12.212.2 inches\newlineActual Value = 10.210.2 inches
  3. Calculate Absolute Difference: Calculate the absolute difference between the measured value and the actual value.\newlineAbsolute Difference = Measured ValueActual Value|\text{Measured Value} - \text{Actual Value}|\newlineAbsolute Difference = 12.2 inches10.2 inches|12.2 \text{ inches} - 10.2 \text{ inches}|\newlineAbsolute Difference = 2.0 inches|2.0 \text{ inches}|
  4. Calculate Percent Error: Calculate the percent error using the formula.\newlinePercent Error = (Absolute Difference/Actual Value)×100%(\text{Absolute Difference} / \text{Actual Value}) \times 100\%\newlinePercent Error = (2.0 inches/10.2 inches)×100%(2.0 \text{ inches} / 10.2 \text{ inches}) \times 100\%\newlinePercent Error = 0.19607843137×100%0.19607843137\ldots \times 100\%
  5. Convert to Percentage: Convert the decimal to a percentage and round to the nearest tenth of a percent.\newlinePercent Error = 19.607843137%19.607843137\ldots\%\newlineRounded Percent Error = 19.6%19.6\%

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