Numerical Tolerance

Explains the difference in tolerance type and numerical tolerance.

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Complete Code

Download file: NumericalTolerance.pg

See Also

PG problem file

Explanation

DOCUMENT();
loadMacros('PGstandard.pl', 'PGML.pl', 'PGcourse.pl');

Preamble

These standard macros need to be loaded. 
$ans1 = Compute('1.5708')->cmp(
    tolType   => 'absolute',
    tolerance => .0001,
);

$ans2 = Compute('1.5708');

Context('Numeric')->flags->set(
    tolerance => 0.0001,
    tolType   => 'absolute',
);

$ans3 = Compute('1.5708');

Setup

This shows three different ways of setting the toltype and tolerance of the answer. The tolType can be absolute (specifying a decimal distance from the correct answer that will be allowed) or relative (specifying a percent error that will be allowed).

Thus if the correct answer is 17, a tolerance of 0.01 will mean that the student answer must be in the interval (16.99,17.01) if the tolType is absolute, and in the interval (16.83,17.17) if tolType is relative (or omitted, as relative tolerance is the default).

  1. The default Context('Numeric') is used (but not needed) and within the Compute call, the tolerance type and level is set.

  2. The tolerance and toltype is set on the answer check with the cmp call. See the problem statement below.

  3. The tolerance and toltype can be set on the Context. This is useful if the desired toltype and/or tolerance is the same for many answer. Typically this would go at the top of the setup section.

BEGIN_PGML
For each of the following Enter your answer accurate to four decimal places .

1. Enter [`` \frac{\pi}{2}= ``] [____]{$ans1}

2. Enter [`` \frac{\pi}{2}= ``] [____]{$ans2->cmp(
    tolType   => 'absolute',
    tolerance => .0001,
)}

3. Enter [`` \frac{\pi}{2}= ``] [____]{$ans3}

END_PGML

Statement

This is the problem statement in PGML. 
BEGIN_PGML_SOLUTION
Solution explanation goes here.
END_PGML_SOLUTION

ENDDOCUMENT();

Solution

A solution should be provided here.