The inexactness that results from doing numerical computations with floating
point numbers often results in much more than a mistake at the last decimal
point. If you're not careful, large errors can occur at crucial points in the
calculation that result in your answer being completely wrong.
If you are careful, though, most engineering problems can be adequately solved
with the 6 digit floating numbers that Mathematica provides by default. In fact,
most engineering problems can be solved with smaller floating point numbers.
The reason is that very few physical measurements can be made with such
accuracy. In view of this, Mathematica will allow you to change the size of the
floating point numbers that it uses.
In this set of exercises, you will use Mathematica to investigate the points that we
made in the last two paragraphs.
The exercises contain five questions, numbered in sequence and displayed in
boldface type. You are to prepare a short report giving the answers to these
questions. For each question, your report should contain the text of the
question as given below, your answer to the question, and the output from Mathematica
that shows how you arrived at your answer.
To prepare this report, you will need to save your Mathematica session to a file as
described earlier in this lesson. Save it to a file called hw.txt. Then
read the file into a text editor and edit it by removing the extraneous parts of the
Mathematica session and adding our questions and your commentary. You will doubtless
want to use the mouse to copy and paste the questions from the notebook into the
text file.