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- Fixes Bug #1313

    1: \label{Tolerance}
    2: A \textbf{tolerance\index{tolerance}} parameter determines how closely
    3: the system will require the student's answer to be in order to count it correct.
    4: 
    5: 
    6: For technical reasons, it is almost never a good idea to set this parameter
    7: to zero. Computers can only approximate computations involving real numbers. For instance,
    8: a computer's {[}decimal{]} answer to the simple problem $\frac{1}{3}$ is
    9: {}``0.33333333333333331''. It \emph{should} be an infinite series of 3's,
   10: and there certainly shouldn't be a {}``1'' in the answer, but no computer
   11: can represent an infinitely long, infinitely detailed real number. Therefore,
   12: for any problem where the answer is not a small integer, you \emph{need}
   13: to allow a tolerance factor, or the students will find it nearly impossible
   14: to exactly match the computers idea of the answer. You may find the
   15: default too large for some problems. 
   16: 
   17: There are
   18: three kinds of tolerance. For some answer $A$ and a tolerance $T$,
   19: 
   20: \begin{enumerate}
   21: \item an \textbf{Absolute} tolerance\index{absolute tolerance}\index{tolerance, absolute}
   22: will take anything in the range $A\pm T$. So if $A=10$ and $T=2$, then
   23: anything between 8 and 12 is acceptable.
   24:  Any number in the tolerance field \emph{without} a \textbf{\%} symbol is
   25: an absolute tolerance.
   26: \item a \textbf{Relative} tolerance\index{relative tolerance}\index{tolerance, relative}
   27: will take anything in the range $A\pm aT$, where \emph{T} is interpreted
   28: as a percentage/100. Any number in the tolerance field \emph{followed by} a \textbf{\%}
   29: symbol is a relative tolerance. For example, $a=10$ and $t=10\%$ will accept
   30: anything between 9 and 11. 
   31: 
   32: \item a tolerance that is a calculated variable (identified by \$ sign as
   33: the first character). For example, if an answer is $\$X$,and for a student
   34: possible values range from $-\$X1$ to $+\$X1$, you could choose $T =
   35: \$tolerance = \$2X1/100;$ acceptable answers would then be from
   36: $\$X-\$tolerance$ to $\$X+\$tolerance$. (This is especially useful when answers
   37: close to zero are possible for some students)
   38: 
   39: \end{enumerate}