A student measures two quantities a and b and obtains the results a=11.5+-0.2cm and b=25.4+-0.2s. She now calculates the product q=ab. Find her anser, giving both its percent and absolute uncertainties, as found using the provisional rule.

Question

fretje · Answer

q = a.b = 11.5*25.4 = 292.1
a has relative error 0.2/11.5 = 1.74%
b has relative error 0.2/25.4 = 0.79%
q has relative error 1.74%+0.79% = 2.527%
thus q has absolute error of 2.527%*292.1=7.38
thus q = 292.1 +-7.38  and rounded 292 +-7cm.s