## WeBWorK Main Forum

### Unexpected decimal places in display of question

by Alice McLeod -
Number of replies: 6
Hi folks!

I did the Webwork authoring PREP course in the summer of 2015, and have been happily writing a few webwork problems for my students since then (nothing terribly ambitious)! I've just run into a weird little problem that I have no idea how to solve, and I'm hoping someone here can help me.

In a nutshell: there's a number which is being calculated in my code and which should be 10, but which is displaying to the student as 9.99999999999999 instead, which is confusing for the student. However, this problem is occurring only for certain seed values; for other students, the numbers are showing up as integers, as expected.

I'm including a code and also a screenshot of the affected student's problem. The seed value for the affected student is 3892. Thanks for any help you can give me!

- Alice McLeod

## Markov chain problem for Linear Algebra (Social Science/Commerce)
## Written by Alice McLeod

DOCUMENT();

"PGstandard.pl",     # Standard macros for PG language
"MathObjects.pl",
"MatrixCheckers.pl",
);

TEXT(beginproblem());

# Show which answers are correct and which ones are incorrect
$showPartialCorrectAnswers = 1; ############################################################## # # Setup # # Context("Numeric"); # Generate the transition matrix do {$a = random(0.1,0.8,0.1);
$b = random(0.1,0.8,0.1); } until ($a+$b<1);$x = 1-$a-$b;

do {
$c = random(0.1,0.8,0.1);$d = random(0.1,0.8,0.1);
} until ($c+$d<1);
$y = 1-$c-$d; do {$e = random(0.1,0.8,0.1);
$f = random(0.1,0.8,0.1); } until ($e+$f<1);$z = 1-$e-$f;

Context("Matrix");

$transition = Matrix( [[$a,$c,$e],[$b,$d,$f],[$x,$y,$z]]);

# convert needed probabilities into percent for inclusion in question

Context("Numeric");
Context()->{format}{number} = "%.1f";

$bper =$b*100;
$xper =$x*100;
$cper =$c*100;
$yper =$y*100;
$eper =$e*100;
$fper =$f*100;

# set up steady state vector

$k1 =$e/(1-$a) - ($c/((1-$a)*$y+$c*$x))*(-$e-$f+($e*$x)/(1-$a));$k2 = -((1-$a)*(-$e-$f)+$e*$x)/($y*(1-$a)+$c*$x);$t = 1/($k1 +$k2 +1);

$q1 =$t*$k1;$q2 = $t*$k2;
$q3 =$t;

Context("Matrix");

$q = Matrix([[$q1], [$q2], [$q3]]);

# convert needed probabilites into percent for final answer

Context("Numeric");

# Tolerance set to allows student to round to nearest whole number
$q1per = Compute($q1*100)->with(
tolType => 'absolute',
tolerance => .51,
);
$q2per = Compute($q2*100)->with(
tolType => 'absolute',
tolerance => .51,
);
$q3per = Compute($q3*100)->with(
tolType => 'absolute',
tolerance => .51,
);

##############################################################
#
#  Text
#
#

Context()->texStrings;
BEGIN_TEXT
Callum always eats either pancakes, chicken or fish for supper. If he has pancakes today, then there's a $bper$PERCENT chance he'll have chicken tomorrow, and a $xper$PERCENT chance he'll have fish tomorrow. If he has chicken today, then there's a $cper$PERCENT chance he'll have pancakes tomorrow, and a $yper$PERCENT chance he'll have fish tomorrow. If he has fish today, then there's a $eper$PERCENT chance he'll have pancakes tomorrow, and a $fper$PERCENT chance he'll have chicken tomorrow.

$BR$BR
Letting "eats pancakes" be state 1, "eats chicken" be state 2, and "eats fish" be state 3, find the transition matrix.
$BR $$P=$$\{$transition->ans_array\}

$BR$BR
In the long term, Callum will eat pancakes about \{ ans_rule(3) \}$PERCENT of the time, chicken about \{ ans_rule(3) \}$PERCENT of the time, and fish about \{ ans_rule(3) \}$PERCENT of the time. END_TEXT Context()->normalStrings; ############################################################## # # Answers # # ANS($transition->cmp() );

ANS($q1per->cmp() ); ANS($q2per->cmp() );

If you redefine $xper to be a MathObject Real, like:$xper = Real($xper); or:$xper = Compute($xper); Then it will still have the same value, but the MathObjects engine will control how to display that number, and will round to 6 significant figures (or fewer --- here you would just see "10".) You may want to do this with all of your variables, because other seeds might lead to other numbers with machine rounding error. In reply to Alex Jordan ### Re: Unexpected decimal places in display of question by Danny Glin - As Alex mentioned, the issue stems from the way perl does calculations with floating point (real) numbers. My preferred solution to this is to do as many of the calculations as you can using integers, and then convert them to decimals as necessary. In your example, I would suggest generating the percentages randomly, then calculating the decimals after. You can also get rid of your while loops by having the bounds on the second variable depend on the first. For example:$aper = random(10,80,10);
$bper = random(10,90-$aper,10);
$xper = 100-$aper-$bper;$a = $aper/100;$b = $bper/100;$x = $xper/100; In reply to Danny Glin ### Re: Unexpected decimal places in display of question by Alice McLeod - Thanks for the tip, Danny! That will come in handy in the future. In reply to Danny Glin ### Re: Unexpected decimal places in display of question by Paul Pearson - Hi Alice, As you might suspect, the decimal to binary conversion (which occurs when numbers are stored internally on your computer hardware) is the culprit of the problem here. Here's a non-MathObjects based solution that should avoid the decimal to binary conversion for things that are displayed directly to the student. Replace$a = random(0.1,0.8,0.1);

by

$a = list_random('0.1','0.2','0.3','0.4','0.5','0.6','0.7','0.8'); Using list_random('string1','string2',...); with quotes around each item makes the value of$a into a perl scalar that gets interpreted as a string first and converted to a perl decimal only when needed.  Unfortunately, there's no "iterative constructor" for list_random(), so you have to list all of the values manually.

A MathObjects-based solution would be to replace

$a = random(0.1,0.8,0.1); by$a = Real(random(0.1,0.8,0.1));

MathObjects is usually smart enough to display to the student only what is sensible.

I don't have time to test either of these solutions for your problem, but it shouldn't take long to see if either (or both) do what you expect.

Best regards,

Paul Pearson

### Re: Unexpected decimal places in display of question

by Alice McLeod -
Hi Paul,

I've actually already implemented Alex's solution, and it worked; I'll leave it at that for the moment, since this assignment is currently live in the hands of students, so I don't want to mess with it too much (in particular, I don't want to risk re-randomizing the numbers out from under the students)!

Once the semester is over and I have time to tidy up my code, I'll come back to this.

Thanks so much for the additional info and suggestions!

(I still have so much to learn...)

- Alice (no programming background, just muddling along here!)