Xavier measured a line to be $15$ . $2$ inches long. If the actual length of the line is $14$ . $9$ inches, then what was the percent error of the measurement, to the nearest tenth of a percent? $\newline$ Answer:________ $\%$

Full solution

Q. Xavier measured a line to be

15

2

inches long. If the actual length of the line is

14

9

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

\newline

Answer:________

\%

Understand formula for percent error: Understand the formula for percent error. $\newline$ The formula for percent error is: $\newline$ Percent Error = $(|\text{Measured Value} - \text{Actual Value}| / \text{Actual Value}) \times 100\%$ $\newline$ Here, the measured value is $15.2$ inches, and the actual value is $14.9$ inches.
Plug values into formula: Plug the values into the percent error formula. $\newline$ Percent Error = $(|15.2 - 14.9| / 14.9) \times 100\%$
Calculate absolute difference: Calculate the absolute difference between the measured value and the actual value. $\newline$ Absolute difference = $|15.2 - 14.9| = 0.3$ inches
Divide difference by actual value: Divide the absolute difference by the actual value. $\text{Division result} = \frac{0.3}{14.9}$
Perform division for decimal form: Perform the division to find the decimal form of the percent error. $\text{Division result} = 0.020134228$
Convert decimal to percentage: Convert the decimal to a percentage. $\newline$ Percent Error = $0.020134228 \times 100\% = 2.0134228\%$
Round percent error: Round the percent error to the nearest tenth of a percent. $\newline$ Rounded Percent Error = $2.0\%$