I've done some more investigation, and modified the script to also print the number from memory out after using sprintf. Here's the code:

#sample data set
$Day = 0;
$Seconds = 35247;
$MicroSeconds = 755605;


#combine times into one variable
$Time = $Day + ($Seconds+$MicroSeconds/1000000)/86400;
$sTime = sprintf("%1.20f",$Time);
#write this time to a file
open(FILE,"> test.txt");
printf FILE ("%1.20f",$Time);
close(FILE);


#read that time back in from file
open(FILE,"< test.txt");
@FileContents = <FILE>;
$FileTime = $FileContents[0];

#calculate diffence from time stored in memory and written to file
$Difference = $Time - $FileTime;

#print results
print "\nFrom Memory: ";
printf("%1.20f",$Time);
print "\nFromsprintf: ";
printf("%1.20f",$sTime);
print "\nFromFile   : ";
printf("%1.20f",$FileTime);
print "\nDifference : ";
printf("%1.20f",$Difference);
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This produced the output:

From Memory: 0.40796013431712963000
Fromsprintf: 0.40796013431712957000
FromFile   : 0.40796013431712957000
Difference : 0.00000000000000005551
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Notice that when I print the variable directly using printf I get the number ending in 63. However, if I use sprintf on that number first, it gets changed to the number ending in 57. Anybody know what is going on?