FormattingDecimals

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Formatting Decimals and Using Logarithms: PG Code Snippet


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

Problem Techniques Index

PG problem file Explanation
DOCUMENT();

loadMacros(
"PGstandard.pl",
"MathObjects.pl"
);

TEXT(beginproblem());

Initialization: Standard.

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

#
# both ln and log are natural log (base e)
#

$a = 6; # or $a = random(3,7,1);

#
# log base e
#
$b = sprintf("%0.3f", ln($a) ); # or log($a)
$solution1 = Real("$b");

$f = Formula("ln(x)"); # or log(x)
$solution2 = $f->eval(x=>$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)
$solution3 = Real("$c");

$g = Formula("ln(x)/ln(10)"); # or log(x)/log(10)
$solution4 = $g->eval(x=>$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.

Note: If we load MathObjects.pl, then log and ln are both defined to be the natural logarithm (base e, not base 10). If we had loaded the older PGauxiliaryFunctions.pl macro instead, then log would be defined as the natural logarithm (base e, not base 10), and ln would be undefined.

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 AddingFunctions for how to define and add a new function to the context so that students can enter it in their answers.

Context()->texStrings;
BEGIN_TEXT

Notice the formatting and rounding differences 
between \( $solution1 \) and \( $solution2 \).
$BR
$BR
Try entering \( \ln($a), \log($a), 
\ln($a)/\ln(10), \log($a)/\log(10),
\mathrm{logten}($a), \mathrm{log10}($a) \).
$BR
$BR
\( \ln($a) = \) \{ ans_rule(20) \}
$BR
\( \ln($a) = \) \{ ans_rule(20) \}
$BR
\( \log_{10}($a) = \) \{ ans_rule(20) \}
$BR
\( \log_{10}($a) = \) \{ ans_rule(20) \}

END_TEXT
Context()->normalStrings;

Main Text: Notice the difference in decimal formatting when "Show Correct Answers" is checked and you click "Submit Answers".

ANS( $solution1->cmp() );
ANS( $solution2->cmp() );
ANS( $solution3->cmp() );
ANS( $solution4->cmp() );

ENDDOCUMENT();

Answer Evaluation: Standard.

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