Question

Layla measured a line to be 6.8 inches long. If the actual length of the line is 6.5 inches, then what was the percent error of the measurement, to the nearest tenth of a percent?

Answer 1

Given parameters:

Measured length = 6.8inches

Actual length = 6.5 inches

Unknown parameter is the percentage error

Errors introduce uncertainty into a reading. Often times measurement errors are incurred in a process due to diverse reasons. This error can be due to the problems with the measuring device, incorrect reporting of measured values and also, the scientist can be at fault.

Deviation from the actual measurement leads to the concept of accuracy.

To solve this problem, we need to find the absolute error;

Absolute error = | Measured length - Actual length|

Input the variables given and solve;

Absolute error = | 6.8 - 6.5| = 0.3 inches

Now, let us find the percentage error;

Percentage error =
`(Absolute error)/(Actual length) x 100`

Input the parameters and solve;

Percentage error =
`(0.3)/(6.5) x 100` = 4.615%

To the nearest tenth percent = 4.6%

Therefore, the percentage error to the nearest tenth percent = 4.6%