Chase measured a line to be $2$ . $8$ inches long. If the actual length of the line is $2$ . $9$ inches, then what was the percent error of the measurement, to the nearest tenth of a percent? $\newline$ Answer:_______ $\%$

Full solution

Q. Chase measured a line to be

2

8

inches long. If the actual length of the line is

2

9

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

\newline

Answer:_______

\%

Understand formula: Understand the percent error formula. $\newline$ Percent error is calculated using the formula: $\newline$ Percent Error = $(|Actual Value - Measured Value| / Actual Value) \times 100$ $\newline$ Here, the actual value is $2.9$ inches, and the measured value is $2.8$ inches.
Plug in values: Plug in the values into the percent error formula. $\newline$ Percent Error = $(|2.9 - 2.8| / 2.9) \times 100$
Calculate absolute difference: Calculate the absolute difference between the actual value and the measured value. $\newline$ Absolute difference = $|2.9 - 2.8| = 0.1$ inches
Divide absolute difference: Divide the absolute difference by the actual value. Division result = $\frac{0.1}{2.9}$
Perform division: Perform the division to find the decimal form of the percent error. Division result = $0.034482758620689655$ (This is a repeating decimal, but we will round it later.)
Convert to percentage: Convert the decimal to a percentage. $\newline$ Percent Error = $0.034482758620689655 \times 100$
Calculate percent error: Calculate the percent error as a percentage. $\newline$ Percent Error = $3.4482758620689655\%$
Round to nearest tenth: Round the percent error to the nearest tenth of a percent. $\newline$ Rounded Percent Error = $3.4\%$