Formatting Decimals

We show how to use format decimals, and, conveniently also how to use logarithmic functions in PG problems.

Complete Code

PG problem file

Explanation

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

Preamble

These standard macros need to be loaded.

Context("Numeric");
Context()->variables->set(x => { limits => [ 2, 4 ] });

$a = random(3, 7, 1);

# both ln and log are natural log (base e)
$b    = sprintf("%0.3f", ln($a));
$ans1 = Real("$b");

$f    = Formula("ln(x)");    # or log(x)
$ans2 = $f->eval(x => $a);

# log base 10 is log10, logten,
# ln(x)/ln(10), or log(x)/log(10)

$c    = sprintf("%0.3f", ln($a) / ln(10));    # or log($a)/log(10)
$ans3 = Real("$c");

$g    = Formula("ln(x)/ln(10)");              # or log(x)/log(10)
$ans4 = $g->eval(x => $a);

Setup

Since the domain of a logarithmic function is all positive real numbers, we should set the domain of function evaluation to [2,4] in order to avoid vertical asymptotes and places where a logarithmic function takes values close to zero.

Use perl’s sprintf( format, number ); command to format the decimal. The "%0.3f" portion truncates after 3 decimal places and uses zeros (not spaces) to right-justify. For answers involving money, you should set "%0.2f" for two decimal places and zero filling (for example, sprintf("%0.2f",0.5); returns 0.50). You can do a web search for more options to perl’s sprintf, and also for WeBWorK’s contextCurrency.pl. If you do further calculations with $b, be aware that numerical error may be an issue since you’ve reduced the number of decimal places.

We used the logarithm change of base formula log10(a) = log(a) / log(10) = ln(a) / ln(10) to get a logarithm base 10.

It is possible to set a context flag that will use the base 10 log via Context()->flags->set(useBaseTenLog=>1); The default is that this is set to zero.

If you would like to define log base 2 (or another base) see Adding Functions to a Context for how to define and add a new function to the context so that students can enter it in their answers.

BEGIN_PGML
Notice the formatting and rounding differences
between [` [$ans1] `] and [` [$ans2] `].

Try entering [` \ln([$a]), \log([$a]), \ln([$a])/\ln(10), \log([$a])/\log(10),
\mathrm{logten}([$a]), \mathrm{log10}([$a]) `].


1. [` \ln([$a]) = `] [_____]{$ans1}

2. [` \ln([$a]) = `] [_____]{$ans2}

3. [` \log_{10}([$a]) = `] [_____]{$ans3}

4. [` \log_{10}([$a]) = `] [_____]{$ans4}
END_PGML

Statement

Notice the difference in decimal formatting when “Show Correct Answers” is checked and you click “Submit Answers”.

BEGIN_PGML_SOLUTION
Solution explanation goes here.
END_PGML_SOLUTION

ENDDOCUMENT();

Solution

A solution should be provided here.