Error Analysis

How to Report and Use Uncertainties

2.2 Rewrite the following answers in their clearest forms, with a suitable number of significant figures:

(a) measured height = 5.03 ± 0.04329 meters;

(b) measured time = 19.5432 ± 1 sec;

(c) measured charge = - 3.21 x 10-19 ± 2.67 x 10-20 coulombs;

(d) measured wavelength = 0.000 000 563 ± 0.000 000 07 meters;

(e) measured momentum = 3.267 x 103 ± 42 gm-cm/sec.

2.3 (a) A student measures the density of a liquid five times and gets the results (all in gm/cm3) 1.8, 2.0, 2.0, 1.9, 1.8. What would you suggest as the best estimate and uncertainty based on his measurements?

(b) He is told that the accepted value is 1.85 gm/cm3. What is the discrepancy (between his best estimate and the accepted value)? Do you think it significant?

2.4 The time for ten revolutions of a turntable is measured by noting the starting and stopping times with the second hand of a wristwatch and subtracting. If the starting and stopping times are uncertain by ± 1 sec each, what is the uncertainty in the time for ten revolutions?

2.13 (a) A student's calculator shows an answer 123.123. If the student decides that this number actually has only three significant figures, what are its absolute and fractional uncertainties?

(b) Do the same for the number 123,123

(c) Do the same for the number 321.321

(d) Do the fractional uncertainties lie in the range expected for three significant figures?

2.14 (a) A student measures two quantities a and b with the results a = 11.5 ± 0.2 cm and b = 25.4 ± 0.2 cm. He now calculates the produce q = a b. Find his answer, giving both its percentage uncertainty and its absolute uncertainty.

(b) Repeat part (a) for the measurements a = 10 ± 1 cm and b = 27.2 ± 0.2 sec.

(c) Repeat part (a) with a = 3.0 ft ± 8% and b = 4.0 lb ± 2%.