There are many ways to solve the problem, but here's a trick that may not leap straight to your finger tips:

use warnings;
use strict;
use bignum;

my $e = 0.00141;
my $o =1;
for (1 .. 10){
    "@{[$o *= $e]}" =~ /(0\.0*\d{0,5})/;
    print "$1\n";
}
[download]

Prints:

0.00141
0.0000019881
0.0000000028032
0.0000000000039525
0.0000000000000055730
0.0000000000000000078580
0.000000000000000000011079
0.000000000000000000000015622
0.000000000000000000000000022027
0.000000000000000000000000000031059
[download]

The @{[...]} trick is useful for interpolating the result of a chunk of code into a string. The rest should be pretty obvious, but note that if the regex doesn't match the print may generate some interesting results.

Update: bah, forgot about the rounding. Oh well, the interpolation trick is still worth knowing even if it doesn't really help solve the OP's problem.