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Olivia measured a line to be 2.2 inches long. If the actual length of the line is 2.3 inches, then what was the percent error of the measurement, to the nearest tenth of a percent?
Answer: 
%

Olivia measured a line to be 22.22 inches long. If the actual length of the line is 22.33 inches, then what was the percent error of the measurement, to the nearest tenth of a percent?\newlineAnswer: _______% \%

Full solution

Q. Olivia measured a line to be 22.22 inches long. If the actual length of the line is 22.33 inches, then what was the percent error of the measurement, to the nearest tenth of a percent?\newlineAnswer: _______% \%
  1. Concept of Percent Error: Understand the concept of percent error.\newlinePercent error is a measure of how inaccurate a measurement is, represented as a percentage of the actual value. The formula for percent error is:\newlinePercent 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.\newlineIn this problem, the measured value is 2.22.2 inches, and the actual value is 2.32.3 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}| = 2.22.3|2.2 - 2.3| = 0.1|-0.1| = 0.10.1 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 = (0.1/2.3)×100%(0.1 / 2.3) \times 100\%
  5. Perform Division and Multiplication: Perform the division and multiplication to find the percent error.\newlinePercent Error = (0.1/2.3)×100%0.04347826087×100%4.347826087%(0.1 / 2.3) \times 100\% \approx 0.04347826087 \times 100\% \approx 4.347826087\%
  6. Round Percent Error: Round the percent error to the nearest tenth of a percent.\newlinePercent Error 4.3%\approx 4.3\%

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