Return to Tolerance.tex CVS log

Up to [LON-CAPA] / loncom / html / adm / help / tex

Annotation of loncom/html/adm/help/tex/Tolerance.tex, revision 1.2

1.2     ! bowersj2    1: \label{Tolerance}
1.1       bowersj2    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: two 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. 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: \end{enumerate}