Difference between revisions of "FormattingDecimals"
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− | <h2>Formatting Decimals: PG Code Snippet</h2> |
+ | <h2>Formatting Decimals and Using Logarithms: PG Code Snippet</h2> |
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− | <em>We show how to format decimals |
+ | <em>We show how to use format decimals, and, conveniently also how to use logarithmic functions in PG problems.</em> |
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Context("Numeric"); |
Context("Numeric"); |
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− | Context() |
+ | Context()->variables->set(x=>{limits=>[2,4]}); |
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− | <b>Setup:</b> |
+ | <b>Setup:</b> |
+ | Since the domain of a logarithmic function is all positive real numbers, we should set the domain of function evaluation to <code>[2,4]</code> in order to avoid vertical asymptotes and places where a logarithmic function takes values close to zero. |
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Use perl's <code>sprintf( format, number );</code> command to format the decimal. The <code>"%0.3f"</code> portion truncates after 3 decimal places and uses zeros (not spaces) to right-justify. For answers involving money, you should set <code>"%0.2f"</code> for two decimal places and zero filling (for example, <code>sprintf("%0.2f",0.5);</code> returns <code>0.50</code>). You can do a web search for more options to perl's <code>sprintf</code>, and also for WeBWorK's <code>contextCurrency.pl</code>. If you do further calculations with <code>$b</code>, be aware that numerical error may be an issue since you've reduced the number of decimal places. |
Use perl's <code>sprintf( format, number );</code> command to format the decimal. The <code>"%0.3f"</code> portion truncates after 3 decimal places and uses zeros (not spaces) to right-justify. For answers involving money, you should set <code>"%0.2f"</code> for two decimal places and zero filling (for example, <code>sprintf("%0.2f",0.5);</code> returns <code>0.50</code>). You can do a web search for more options to perl's <code>sprintf</code>, and also for WeBWorK's <code>contextCurrency.pl</code>. If you do further calculations with <code>$b</code>, be aware that numerical error may be an issue since you've reduced the number of decimal places. |
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Note: If we load <code>MathObjects.pl</code>, then <code>log</code> and <code>ln</code> are both defined to be the natural logarithm (base e, not base 10). If we had loaded the older <code>PGauxiliaryFunctions.pl</code> macro instead, then <code>log</code> would be defined as the natural logarithm (base e, not base 10), and <code>ln</code> would be undefined. |
Note: If we load <code>MathObjects.pl</code>, then <code>log</code> and <code>ln</code> are both defined to be the natural logarithm (base e, not base 10). If we had loaded the older <code>PGauxiliaryFunctions.pl</code> macro instead, then <code>log</code> would be defined as the natural logarithm (base e, not base 10), and <code>ln</code> would be undefined. |
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+ | It is possible to set a context flag that will use the base 10 log via <code>Context()->flags->set(useBaseTenLog=>1);</code> The default is that this is set to zero. |
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Latest revision as of 10:40, 7 May 2012
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.
PG problem file | Explanation |
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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
Use perl's We used the logarithm change of base formula log_{10}(a) = log(a) / log(10) = ln(a) / ln(10) to get a logarithm base 10.
Note: If we load
It is possible to set a context flag that will use the base 10 log via 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. |