Expressing Experimental Error If the accepted value of π is 3.1416, what are the fractional error and the percent error of the experimental value found it 1.e? In an experiment to measure the acceleration g due to gravity, two values, 9.96 m/s2 and 9.72 m/s2, are determined. Find (1) the percent difference of the measurements, (2) the percent error of each measurement, and (3) the percent error of their mean. The accepted value for g is 9.80 m/s2. (show work!!)

1) Δx  = 0.16 m / s² ,   Δx = 9.72-9.8 = 0.08 m / s²

2)  e% = 1.63% , ,   e% = 0.816%

3)           1e% = 0.04

Explanation:

The fractional error in a quantity is the absolute error between the accepted value of the quantity and the percentage error is the fractional error per 100

In this case, it is not indicated which is the measured experimental value of pi, suppose that a value of 3.142 is measured

fractional error

                 e = (ax - ax_average) / x_average

                 e = (3.142 - 3.1416) / 3.1416

                 e = 1.27 10⁻⁴

the percentage error is

                 % = e 100

                 % = 1.27 10-4 100

                 % = 1.27 10⁻²%

1) Δx = 9.96-9.8 = 0.16 m / s²

            Δx = 9.72-9.8 = 0.08 m / s²

2) the percentage difference

 x = 9.96 m / s2

             e% = (9.96 - 9.80) / 9.80 100

             e% = 1.63%

x = 9.72 m / s2

             e% = (9.72 -9.80) / 9.80 100

              e% = 0.816%

3) the mean value is

                x_average = (x1 + x2) / 2

               x_average = (9.96 + 9.72) / 2

               x_average = 9.84 m / s2

               e% = (9.84 - 9.80) / 9.80 100

             1e% = 0.04