How do I set the floating point precision in Perl?

Use Math::BigFloat or bignum:

use Math::BigFloat;
Math::BigFloat->precision(-3);

my $x = Math::BigFloat->new(1.123566);
my $y = Math::BigFloat->new(3.333333);

Or with bignum instead do:

use bignum ( p => -3 );
my $x = 1.123566;
my $y = 3.333333;

Then in both cases:

say $x;       # => 1.124
say $y;       # => 3.333
say $x + $y;  # => 4.457

There is no way to globally change this.

If it is just for display purposes then use sprintf("%.3f", $value);.

For mathematical purposes, use (int(($value * 1000.0) + 0.5) / 1000.0). This would work for positive numbers. You would need to change it to work with negative numbers though.