Evaluate the manager’s calculations with regard to significant digits. If necessary, rewrite any steps, recalculating with the adjusted quantities. For any step that you have to rewrite, explain why the manager’s calculation is in error. (b) Should the manager regard the answer to the calculation in (a) as a perfect measure of the number of ball bearings in the container? (c) How could the manager have changed his procedure to yield an answer with a greater number of significant figures? (d) What is the purpose of paying attention to significant digits in calculations with measured quantities?
A garage manager must determine the number of
metal ball bearings (BBs) in a stock container by mass
measurements. He counts out 5 BBs and finds their
total mass to be 1.9 g. He also finds the total mass
of the stock container and the BBs to be 239.3 g and
the mass of an identical, empty stock container to
be 115.8 g. The store manager then uses his data to
calculate the number of BBs in the stock container:
Average mass of one BB = 1.9/5 = 0.4 g
Mass of BBs in container = 239.3 g - 115.8 g = 123.50 g
Number of BBs in container = 123.50/0.4 g= 300 BBs
(a) Evaluate the manager’s calculations with regard to
significant digits. If necessary, rewrite any steps,
recalculating with the adjusted quantities. For
any step that you have to rewrite, explain why the
manager’s calculation is in error.
(b) Should the manager regard the answer to the
calculation in (a) as a perfect measure of the
number of ball bearings in the container?
(c) How could the manager have changed his
procedure to yield an answer with a greater
number of significant figures?
(d) What is the purpose of paying attention to
significant digits in calculations with measured
quantities?
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