printf "%.5f\n", (1.5553 - 1.5552);
printf "%.5f\n", (0.9984 - 0.998);
printf "%.5f\n", (100.25 - 100.3);
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prints:

0.00010
0.00040
-0.05000
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printf in the instance you have shown doesn't give me anything I can work with
I should have mentioned that the rates are comming in live 24/7 and I want to look at the base point movement as the rates change.
In the examples above I'm looking to see the base point movements of +1,+4 and -5.
Whatever solution I have to get this number must be simple enough that I can use in a function where any number with any number of decimal places is looked at and the difference to last known rate instance is calculated.

In the examples above I'm looking to see the base point movements of +1,+4 and -5.

I'm not really sure I understand, but maybe something like this?

#!/usr/bin/perl

use strict;
use warnings;

print base_point_movement($_),"\n" for (
          1.5553 - 1.5552,
          0.9984 - 0.998,
          100.25 - 100.3,
      );

sub base_point_movement {
    my $diff = shift;
    (sprintf "%+e", $diff) =~ /([+-]\d)\./;
    return $1;
}
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Output:

+1
+4
-5
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Update: as has been pointed out, this only works for +/-9 — which is not too surprising, as it just extracts the before-comma digit of the difference in exponential floating-point representation  (not knowing what a "base point" is defined as, I figured it might suffice...).

Anyhow, here's another variant, kind of extending the idea to what might have been meant — though honestly, I don't have the foggiest whether that's what the OP had in mind.  (Of course, this will also run into problems when the number of significant digits exceeds floating-point precision.)

sub base_point_movement {
    my $bpm = sprintf "%+e", shift;
    $bpm =~ s/0*e.*$//;
    $bpm =~ tr/.//d;
    return $bpm;
}

print base_point_movement($_),"\n" for (
          1.5553    - 1.5552,      # +1
          1.5553    - 1.55,        # +53
          1.56      - 1.55,        # +1
          155.53    - 155.52,      # +1
          15553     - 15552,       # +1
          1555300   - 1555200,     # +1
          1555300   - 155520,      # +139978
          1555.300  - 1555.20,     # +1
          1555300   - 1555201,     # +99
          1.5553    - 1.555201,    # +99
          1.5553    - 1.55521,     # +9
          1.5553    - 1.555301,    # -1
          1.5553    - 1.55530101,  # -101
          1.5553    - 1.5553101,   # -101
          15553     - 15552.9999,  # +1
          15553.001 - 15552.999,   # +2
          15553.001 - 15552.9999,  # +11
          15553.1   - 15552.99,    # +11
          # etc. (you get the idea :)
      );
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I don't understand why you can't simply use subtraction, regardless of the decimal truncation in either of the operands.

You're going to end up with some floating-point drift anyway; perhaps it would be a good idea to drop the decimal points and treat everything as integers, then divide by 10ⁿ when it's time to display the number to the user. (This is the recommended way of doing currency calculations so floating point error doesn't mess with your cents.)

Yes...and I feel stupid that I can't work it out...should be a simple mathematical equation.

my $diff = ($new*10000) - ($old*10000);
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Or if you want to round it,

my $diff = 0 + sprintf '%.0f', ($new*10000) - ($old*10000);
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Update: The *10000 can be factored out: ($new-$old)*10000