Question

When non-metric units were used in the United Kingdom, a unit of mass called the pound-mass (lbm) was employed, where 1 lbm=0.4539 kg. (a) If there is an uncertainty of 0.0001 kg in the pound-mass unit, what is its percent uncertainty? (b) Based on that percent uncertainty, what mass in pound-mass has an uncertainty of 1 kg when converted to kilograms?

a) (a) 0.022%, (b) 220 lbm
b) (a) 0.022%, (b) 22 lbm
c) (a) 2.2%, (b) 220 lbm
d) (a) 2.2%, (b) 22 lbm

Answer 1

The percent uncertainty of the pound-mass unit is 0.022%. The mass in pound-mass that has an uncertainty of 1 kg when converted to kilograms is 4545.4545 lbm.

Step-by-step explanation:

The percent uncertainty can be calculated by dividing the uncertainty by the value of the pound-mass unit and multiplying by 100. In this case, the uncertainty is 0.0001 kg and the pound-mass unit is 0.4539 kg. So, the percent uncertainty is (0.0001 kg / 0.4539 kg) x 100 = 0.022%.

To determine the mass in pound-mass that has an uncertainty of 1 kg when converted to kilograms, we divide the uncertainty of 1 kg by the percent uncertainty of 0.022%. So, the mass in pound-mass is (1 kg / 0.022%) = 4545.4545 lbm.