Solver Converting to and from percents, decimals, and fractions

Source code of 'Converting to and from percents, decimals, and fractions'

This Solver (Converting to and from percents, decimals, and fractions) was created by by jim_thompson5910(35256)

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==section input
This solver will guide you through converting to and from decimals, percents, and fractions (note: I'm still working on the decimals to fractions portion). There are many rules for inputting values (too many to state here), so follow any rules that are presented (if they come up). Try your best to input the numbers and (hopefully) this solver will catch any errors.

Enter the given number (either a fraction, decimal, or whole number) and choose the method of conversion.

Input: *[input my_input=20]

Go from *[choice start percents decimals fractions] to *[choice end decimals fractions percents]
==section solution

perl

### Note: maybe throw in ratios?

############ Start Subroutines

sub gcf {
  my ($x, $y) = @_;
  ($x, $y) = ($y, $x % $y) while $y;
  return $x;
}

sub reduce{

my @arr1=@_;
my @original_arr1=@arr1;

if($arr1[0]==0)
{return $arr1[0];}

if($arr1[1]!=0)
{
  my $gcf=gcf($arr1[0],$arr1[1]);
  #$exported_gcf=$gcf;
  $arr1[0]/=$gcf;
  $arr1[1]/=$gcf;
}

return "$arr1[0]/$arr1[1]";
}

sub round
{
 die "Only two arguments are accepted here: num to be rounded and number of places to round to" if @_!=2;
 my ($num,$precision)=@_;
 return $num if $num!~m/\./;
 die "precision must be positive" if $precision<0;
 
 my ($whole, $decimal_portion)=split(/\./,$num);
 my @digits_after_decimal=split(//,$decimal_portion);
 if($precision==0)
 {
 return ++$whole if $digits_after_decimal[0]>=5;
 return $whole if $digits_after_decimal[0]<5;
 }
 else
 { 
 if($digits_after_decimal[$precision]>=5)
 { 
 $digits_after_decimal[$precision-1]++;
 }
 
 $new_decimal_portion=""; 
 for(my $i=0;$i<$precision;$i++)
 {
 $new_decimal_portion.="$digits_after_decimal[$i]";
 }
 $new_decimal_portion=~s/0+$//; ## remove any trailing zeros
 
 return "$whole.$new_decimal_portion";
 
 }
}

############ End Subroutines

############ Start Error Checking

my @tokens=split(//,$my_input);
my ($radix_count, $bar_count)=(0,0);
for(my $i=0;$i<@tokens;$i++)
{
 $radix_count++ if $tokens[$i] eq '.';
 $bar_count++ if $tokens[$i] eq '/';
}
if($radix_count>1)
{
 print "Too many decimal points";
 return;
}
if($bar_count>1)
{
 print "Too many fraction or division bars";
 return;
}

if($my_input=~m/\/0$/)
{
 print "Error: You CANNOT divide by zero. Please correct your input.";
 return;
}

if($my_input=~m/\D\D/)
{
 print "Error: too many symbols or symbols in wrong place/order.";
 return;
}

if($my_input=~m/^\//)
{
 print "Error: You forgot to enter the numerator.";
 return;
}

if($my_input=~m/\/$/)
{
 print "Error: You forgot to enter the denominator.";
 return;
}

if($my_input!~m/\d/)
{
 print "Error: You forgot to enter the number.";
 return;
}

if($my_input eq '')
{
 print "Error: You didn't enter anything.";
 return;
}

my $temp_input=$my_input;
$temp_input=~s/\/|\.//g;
if($temp_input=~m/\-/)
{
 print "Please enter positive numbers.";
 return;
}
if($temp_input=~m/\D/)
{
 print "Please enter whole numbers, decimal values, or fractions (ie no variables or any other symbols)";
 return;
}

$my_input="$my_input.0" if $my_input=~m/\.$/;   ### make 5. ---> 5.0
$my_input="0.$my_input" if $my_input=~m/^\./;   ### make .5 ---> 0.5

############ End Error Checking

if($start eq $end)
{
 print "Note: There's not much work to do in converting $start to $end (as they are the same)...please try again.";

return;
}

my $ans="";

#### Convert percent into a decimal

if(($start eq 'percents') and ($end eq 'decimals'))
{
 if($my_input=~m/\//) ## if input is a fraction
 {
 print "Please convert the fraction to a decimal first (you can use this solver to do so).";
 return;
 }
 $ans=$my_input/100;
 print "

To find the decimal equivalent of $my_input\%, simply divide that value by 100 to get {{{$my_input/100=$ans}}}.

Take note that all that we're doing here is moving the decimal point 2 places to the left to go from $my_input to $ans.

So $my_input\% is equivalent to the decimal value of $ans

";
}

#### Convert percent into a fraction
if(($start eq 'percents') and ($end eq 'fractions'))
{
   if($my_input=~m/\./)
   {
      print "Is \'$my_input\' a decimal or is it a fraction (you might have made a typo somewhere)? If it is both, then please use a calculator to convert it to a decimal number (or maybe to a fraction).";
      return;
   }
   my ($num,$denom)=split(/\//,$my_input);
   $denom=1 if $denom eq '';
   $ans=reduce($num,100);
   print "

To convert the percent $my_input\% into a fraction, simply place that percentage over 100 and reduce the fraction. So place the value $my_input (the given percentage) over 100 to get {{{$my_input/100=$ans}}}

So the percent $my_input\% is equivalent to the fraction {{{$ans}}}

";
}

#### Convert fraction into a decimal
if(($start eq 'fractions') and ($end eq 'decimals'))
{
 if($my_input!~m/\//)
 {
 print "You're missing the fraction bar for the input \'$my_input\'";
 return;
 }
 my ($num,$denom)=split(/\//,$my_input);
 $denom=1 if $denom eq '';
 $ans=$num/$denom;
 $ans=round($ans,3);
 print "

Simply use a <a href=\"http://my.hrw.com/math06_07/nsmedia/tools/Sci_Calculator/Sci_Calculator.html\">calculator</a> or <a href=\"http://en.wikipedia.org/wiki/Long_division\">long division</a> to convert the given fraction {{{$my_input}}} to a decimal number. In this case, {{{$my_input=$ans}}}

";
}

#### Convert fraction into a percent
if(($start eq 'fractions') and ($end eq 'percents'))
{
 if($my_input=~m/\./)
 {
 print "Please enter whole numbers or fractions (where both the numerator and denominator are whole numbers).";
 return;
 }
 if($my_input!~m/\//)
 {
 print "You're missing the fraction bar for the input \'$my_input\'";
 return;
 }
 my ($num,$denom)=split(/\//,$my_input);
 $denom=1 if $denom eq '';
 my $dec=$num/$denom;
 $dec=round($dec,3);
 my $ans=100*$dec;
 my $new_num=$num*100;
 print "

There are two ways to do this

Method #1:

First, we must convert the given fraction into a decimal number. So use a calculator or long division to convert the given fraction {{{$my_input}}} to a decimal number. In this case, {{{$my_input=$dec}}}

Now just multiply the equivalent decimal {{{$dec}}} by 100 to convert it into a percent. So {{{100*$dec=$ans}}}. Take note that we're simply moving the decimal point two spots to the right.

So the given fraction {{{$my_input}}} is equivalent to $ans\%

--------------------------

Or...

Method # 2

Recall that a percent can be represented by the equation

<pre>

percent           part
------------- = ----------------
    100              whole

</pre>

where \'percent\' is the answer we want, the \'part\' is the numerator of the given fraction, and \'whole\' is the denominator of the given fraction.

So let's make \'x\' the unknown percentage.

Since we're given the fraction {{{$my_input}}}, this means that the numerator is {{{$num}}} and the denominator is {{{$denom}}}. Using the equation above, we see that the \'part\' is {{{$num}}} while the \'whole\' is {{{$denom}}}

So let\'s plug these values into the equation given above to get {{{x/100=$num/$denom}}}

{{{x/100=$num/$denom}}} Start with the given equation

{{{cross(100)(x/cross(100))=100($num/$denom)}}} Multiply both sides by 100 to isolate \'x\'.

{{{x=100($num/$denom)}}} Simplify

{{{x=(100*$num)/$denom}}} Multiply 100 and {{{$num/$denom}}} to get {{{(100*$num)/$denom}}}

{{{x=$new_num/$denom}}} Multiply 100 and {{{$num}}} to get {{{$new_num}}}

{{{x=$ans}}} Divide

So the given fraction {{{$my_input}}} is equivalent to $ans\%

";
}

#### Convert decimals into a fraction
if(($start eq 'decimals') and ($end eq 'fractions'))
{

print "This part is still under construction. In the meantime, check out this <a href=http://www.mindspring.com/~alanh/fracs.html>decimals to fractions</a> calculator. ";

}

#### Convert decimals into a percent
if(($start eq 'decimals') and ($end eq 'percents'))
{ 
 if($my_input=~m/\//) ## if input is a fraction
 {
 print "Only enter decimal values (ie no fractions).";
 return;
 }
 #if($my_input!~m/\./)
 #{
 # print "The decimal value of $my_input is simply {{{$my_input/1}}} (since this number is a #whole number).";
 # return $my_input;
 #}
 print " To convert the decimal value {{{$my_input}}} into a percent, multiply it by 100: {{{$my_input*100=",$my_input*100,"}}}. So the decimal value {{{$my_input}}} is equivalent to ",$my_input*100,"\% ";
}

print "
Click <a href=\"http://my.hrw.com/math06_07/nsmedia/tools/Sci_Calculator/Sci_Calculator.html\">here</a> if you need a calculator.

==section output
ans

==section check