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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}
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