#!/usr/bin/perl -w
...
use warnings;
...
BEGIN { $^W = 1; }
sub BEGIN {
    if ($^W == 1) {say "Let's get started..."}
    else {die $@}
}
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Why do you want to turn on warnings 3 times and then die if they're not turned on? use warnings; is sufficient for anything but an ancient version of perl, in which case you might need the -w switch.

my $resistance = <STDIN>;
if ($current =~ /mA/) {
    $current =~ s/mA//;
    $current =~ s/(^\s+| )//;
    $current /= 1000;
}
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That's kind of a mess. First you match on mA and then remove mA, not to mention that it will fail on bad input. Consider an answer like 0 or "more amps than you'll ever know!" It's much better to extract the expected input and complain if you can't find it. The following is a quick, untested example...

my $input = <STDIN>;
my ($current) = $input =~ /^\s*[\d.]+\s+/ or do {
    error_stuff();
    ... # next, redo, or return, as appropriate
};
$input =~ /\s+mA\s*$/ and $current /= 1000;
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