Gianna measured a line to be $19$ inches long. If the actual length of the line is $17$ . $1$ inches, then what was the percent error of the measurement, to the nearest tenth of a percent? $\newline$ Answer:__________ $\%$

Full solution

Q. Gianna measured a line to be

19

inches long. If the actual length of the line is

17

1

inches, then what was the percent error of the measurement, to the nearest tenth of a percent?

\newline

Answer:__________

\%

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 = $(|\text{Measured Value} - \text{Actual Value}| / \text{Actual Value}) \times 100\%$
Identify Values: Identify the measured value and the actual value. $\newline$ Measured Value = $19$ inches $\newline$ Actual Value = $17.1$ inches
Calculate Absolute Difference: Calculate the absolute difference between the measured value and the actual value. $\newline$ Absolute Difference = $|\text{Measured Value} - \text{Actual Value}|$ $\newline$ Absolute Difference = $|19 - 17.1|$ $\newline$ Absolute Difference = $1.9$ inches
Calculate Percent Error: Calculate the percent error using the formula. $\newline$ Percent Error = $(\text{Absolute Difference} / \text{Actual Value}) \times 100\%$ $\newline$ Percent Error = $(1.9 / 17.1) \times 100\%$
Perform Division and Multiplication: Perform the division and multiplication to find the percent error. $\newline$ Percent Error = $(1.9 / 17.1) \times 100\%$ $\newline$ Percent Error $\approx 0.1111 \times 100\%$ $\newline$ Percent Error $\approx 11.11\%$
Round Percent Error: Round the percent error to the nearest tenth of a percent. $\newline$ Rounded Percent Error = $11.1\%$