We want to calculate a number S. I ask the students to find an interval [a,b] that contains S, and enter the numbers a and b in different boxes. Then I ask them to express their answer like a physicist, by entering S as m plus-or-minus epsilon, where m is the midpoint of [a,b] and epsilon is the radius.

Heartbreak occurs in the following scenario. First, the student finds an interval [a',b'] whose endpoints are within some relative tolerance of the true endpoints, and WW marks their interval correct. Second, the student calculates m', the midpoint of [a',b'] and epsilon', the corresponding radius. Of course m' is close enough to m to get marked right also, but the relative error in epsilon' is enormous and that answer gets marked wrong. I'm not asking about the math here, but rather the psychology. The student thinks they are doing a simple manipulation on a bunch of ingredients that WW has endorsed and inexplicably getting marked wrong. I sympathize with their frustration.

Now for the questions.

1. One obvious solution is to insist on more accuracy in the computation of the original interval, so wrong answers can't be accepted by mistake. What is the approved PGML way to do this? (Can it be done inline, through some modification to the familiar [`a=`][_____]{$answer_a} ?)

2. Does WW include a context or format for numbers that triggers one of those helpful yellow text-box replies saying something like, "Your answer looks pretty close but I'm not going to accept it until you show some more significant digits"?

Thanks! (PS: For forum purposes, I would much rather be answered like a beginner than like an expert. Extra thanks if you kindly take on that extra challenge!!)