College Physics Problem 1.26

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?

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a) The percent uncertainty of the lbm is

%  unc_{lbm}=frac{0.0001 kg}{0.4539 kg}times 100%

%  unc_{lbm}=0.022 %

b) For an uncertainty of 1 kg, the corresponding lbm is

lbm=frac{delta lbm}{% unc_{lbm}}}times 100 %

lbm=frac{1 kg}{0.02 %} times frac{1 lbm}{0.4539 kg} times 100 %

lbm=11015.64 lbm

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