Cool exercise for scientific notation and significant figures

Author: John
Lesson Plan:

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worksheet for significant figures and scientific notation.


A manufacturer of aluminum foil makes strips 1.500 meters wide.  They are wrapped onto rolls in lengths of 500 meters.  The manufacturer is concerned about the thickness of the foil and tests the thickness by weighing the completed rolls.  The thickness must be between 0.001500 and 0.001600 centimeters.


A roll as described above weighs 36.64 kilograms.  Of this, the empty spool weighs 5 kilograms.   The company uses a density of aluminum as 2.704 grams per cubic centimeter.


Calculate the thickness of the foil using scientific notation and appropriate significant figures.  Does this foil meet specifications?


Density =  grams / cubic centimeters

1 meter = 1 x 102 centimeters

1 kilogram = 1 x 103 grams



This company makes between 200 and 250 of these rolls every eight hour shift and they continually test the spools at random.  The rolls always have the same length and width of aluminum foil.  The empty spools always weigh the same.


In order to simplify the procedure, increase efficiency and save money the company wants the thickness specifications calculated for the total weight of the final rolls.  What is the heaviest the rolls could be and what is the lightest the rolls could be to meet the specifications described above.




for the teacher



This problem is interesting and not particularly easy.  It could be applied to many subjects, but was written for chemistry.  


There are two problems.  First, the units are a mess.  Second,  scientific notation will make it much neater. Notice that the weight of the spool is subtracted first.  


The definition of significant figures is: "those values that are known plus one which may be uncertain"  .  Of the 1.5601, clearly the 1 is uncertain.  I would consider the correct answer to be 0.00156 cm.  I notice that the original worksheet is not correct.  The appropriate significant figures can be a product of rigorous statistical analysis, but is often produced by a gut feeling.


If the units are followed carefully, they will fall out  correctly in the answer.


The roll is within specifications.


question II


This is a simple matter of  inserting the two limits into the formula and calculating the final weight.  Do not forget the weight of the spool.