--- loncom/html/adm/help/tex/Tolerance.tex	2013/07/05 18:30:40	1.4
+++ loncom/html/adm/help/tex/Tolerance.tex	2013/07/08 03:29:27	1.5
@@ -1,21 +1,23 @@
 \label{Tolerance}
 A \textbf{tolerance\index{tolerance}} parameter determines how closely
-the system will require the student's answer to be in order to count it correct. 
-The tolerance parameter should always be defined for a numerical problem.
+the system will require the student's answer to be in order to count it correct.
+The tolerance will default to zero if it is not defined.
+The tolerance parameter should always be defined for a numerical problem 
+unless you are certain only integer answers are generated from your script and 
+you want students to reply with exactly that integer.
 
-For technical reasons, it is almost never a good idea to set this parameter
-to zero. Computers can only approximate computations involving real numbers. For instance,
+If the computer answer is a floating point number, the tolerance should not 
+be zero. Computers can only approximate computations involving real numbers. For instance,
 a computer's {[}decimal{]} answer to the simple problem $\frac{1}{3}$ is
 {}``0.33333333333333331''. It \emph{should} be an infinite series of 3's,
 and there certainly shouldn't be a {}``1'' in the answer, but no computer
 can represent an infinitely long, infinitely detailed real number. Therefore,
-for any problem where the answer is not a small integer, you \emph{need}
+for any problem where the answer is not an integer, you \emph{need}
 to allow a tolerance factor, or the students will find it nearly impossible
-to exactly match the computers idea of the answer. You may find the
-default too large for some problems. 
+to exactly match the computer's idea of the answer. You may find the
+default tolerance too large for some problems, so adjust as appropriate. 
 
-There are
-three kinds of tolerance. For some answer $A$ and a tolerance $T$,
+There are three kinds of tolerance. For some answer $A$ and a tolerance $T$,
 
 \begin{enumerate}
 \item an \textbf{Absolute} tolerance\index{absolute tolerance}\index{tolerance, absolute}
@@ -37,3 +39,22 @@ $\$X-\$tolerance$ to $\$X+\$tolerance$.
 close to zero are possible for some students)
 
 \end{enumerate}
+
+Some care is necessary when setting the display format of the computer answer. 
+Before testing the tolerance, LON-CAPA converts the computer answer,
+as generated in the script block, according to the
+format attribute in the numericalresponse tag.
+
+Next, the formatted compuer answer is "graded" relative to the significant 
+figures parameter, if it is set (see section \ref{Significant_Figures}. 
+If that test was passed, then a numerical comparison of the Computer's
+answer is made with the range of values:
+
+(\$computerAnswer - \$tolerance) < \$formattedcomputerAnswer <
+(\$computerAnswer + \$tolerance)
+
+If the \$formattedcomputerAnswer satisfies the permitted range, then
+"correct" is returned for the computer answer. It is good idea to test multiple
+randomizations to make sure that your tolerance is compatible with the display format.
+
+