Math – Applications for Living III

In class this week, we talked about ‘precision’.  Even though many of our math classes ignore this topic, students relate to it reasonably well.

One example — find the area of a rectangle that is 3.6 meters wide and 4.2 meters long.  The correct answer is ’15 square meters’, since each measurement has only 2 significant digits.  Calculating ‘15.12’ is only part of the story.  How this 15 square meters is used depends on the purpose for finding the area.  If we are estimating the amount of time needed to paint the area, it is fairly safe to work with 15 square meters … however, if we are buying the paint, we might do better with 20 square meters (1 significant digit).

Several students in class have been dealing with the concept of significant digits in their science class as well … isn’t it nice when people can see an immediate use for what we cover in math class?

The topic of significant digits is a natural whenever we cover geometry.  However, we tend to do a bad job with this; I suspect that we are too concerned about ‘keeping things simple enough’.  One of the larger errors on our part is the treatment of π.  In many books and courses, students are told to use ‘3.12’ as the value of this number regardless of the precision of the other numbers involved.  As you know, the correct process is to use all available digits and round the final answer to the appropriate number of digits.  The irony is that almost all students have access to the value of π to 10 or more digits (calculator or computer).  Let’s start doing good mathematics by having students use the built-in constant instead of the (always inappropriate) approximation.  [It’s always inappropriate because we are not supposed to round intermediate values.]

Another example from class: “A city has a deficit of 43.8 million dollars.  How much per person is this if the city has a population of 136,500?”   As a division, we can calculate any number of digits; many students would ‘naturally’ round the result to the nearest cent ($320.88), though this is not the correct value.  We often say ’round money to the nearest cent’, and this is quite appropriate with interest calculations.  However, it may not be appropriate in many other applications.

The topic of ‘significant digits’ (precision) is appropriate for most math classes, and is accessible to almost all students.

 
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