Question

We are given a=73.8(±2%),b=24.5(±0.8%), and z=ab. Find the following:

(a) the most-likely value of z.
(b) the percent uncertainty in z
(c) the absolute uncertainty in z.
(d) In a single statement, express the most-likely value of z along with the absolute and percent uncertainties.

Answer 1

The most-likely value of z is 1801.1, with an absolute uncertainty of 50.43 and a percent uncertainty of 2.8%.

Step-by-step explanation:

(a) To find the most-likely value of z, we multiply the given values of a and b: z = ab = (73.8)(24.5) = 1801.1.

(b) To find the percent uncertainty in z, we add the percent uncertainties of a and b: percent uncertainty in z = percent uncertainty in a + percent uncertainty in b = 2% + 0.8% = 2.8%.

(c) To find the absolute uncertainty in z, we multiply the most-likely value of z by the percent uncertainty expressed as a decimal: absolute uncertainty in z = (2.8/100) * 1801.1 = 50.43.

(d) The most-likely value of z is 1801.1, with an absolute uncertainty of 50.43 and a percent uncertainty of 2.8%.