Julia measured a line to be 17.6 inches long. If the actual length of the line is 17.8 inches, then what was the percent error of the measurement, to the nearest tenth of a percent?
The percent error can be calculated by taking the absolute error (the absolute value of the difference between the measured value and the actual value) and then dividing by the actual value, finally multiplying by 100 to get the percentage.
Absolute error = |Measured Value - Actual Value|
Percent error = (Absolute error / Actual Value) * 100
Applying the values we have:
Absolute error = |17.6 inches - 17.8 inches| = |0.2| inches = 0.2 inches
Percent error = (0.2 inches / 17.8 inches) * 100
Now we can calculate the percent error:
Percent error = (0.2 / 17.8) * 100 ≈ 1.1235955056%
To round to the nearest tenth of a percent:
Percent error ≈ 1.1%
So the percent error of the measurement to the nearest tenth of a percent is 1.1%.