Just for completeness, I tested it with python and tcl to see if the underlying Tk has a problem. Both worked without problem.

I did test it on perl 5.24.0 with the following code:

#!/usr/bin/perl -w
use warnings;
use strict;
use Tk;
use Devel::Peek;

my $scale = 22.5;
my $x = 14;
my $foo = $x * $scale; # use in numeric context (set NV and IV)
my $sb = 22.5 * 14;
my $i=0;
print "\n0 str: <$scale> / num: <".(0+$scale)."> product $foo should b
+e $sb\n";
Dump($scale);

my $mw = MainWindow->new;
$mw->Entry(-textvariable=>\$scale)->pack;
$mw->bind("<Key-Return>",\&calc);

MainLoop;


sub calc {
    $foo = $scale * $x;
    my $s2 = $scale.' ';
    my $foobar = $s2 * $x;
    $i++;
    print "\n$i str: <$scale> / num: <".(0+$scale)."> product $foo str
+ingified $foobar should be $sb\n";
    Dump($scale);

}
[download]

This seemed to work originally. If you just hit enter a couple of times it fails with:

0 str: <22.5> / num: <22.5> product 315 should be 315
SV = PVNV(0x19572d0) at 0x1982d20
  REFCNT = 2
  FLAGS = (NOK,pIOK,pNOK)
  IV = 22
  NV = 22.5
  PV = 0x196fa80 "22.5"\0
  CUR = 4
  LEN = 32

1 str: <22.5> / num: <22> product 315 stringified 315 should be 315
SV = PVMG(0x1ed5f60) at 0x1982d20
  REFCNT = 3
  FLAGS = (GMG,SMG,IOK,NOK,POK,pIOK,pNOK,pPOK,UTF8)
  IV = 22
  NV = 22.5
  PV = 0x196fa80 "22.5"\0 [UTF8 "22.5"]
  CUR = 4
  LEN = 32
  MAGIC = 0x1fa6a30
    MG_VIRTUAL = &PL_vtbl_uvar
    MG_TYPE = PERL_MAGIC_uvar(U)
    MG_LEN = 24
    MG_PTR = 0x1f24b40 "\260(=\252\254\177\0\0\20==\252\254\177\0\0\0j
+\372\1\0\0\0\0"

2 str: <22.5> / num: <22> product 308 stringified 315 should be 315
SV = PVMG(0x1ed5f60) at 0x1982d20
  REFCNT = 3
  FLAGS = (GMG,SMG,IOK,NOK,POK,pIOK,pNOK,pPOK,UTF8)
  IV = 22
  NV = 22.5
  PV = 0x196fa80 "22.5"\0 [UTF8 "22.5"]
  CUR = 4
  LEN = 32
  MAGIC = 0x1fa6a30
    MG_VIRTUAL = &PL_vtbl_uvar
    MG_TYPE = PERL_MAGIC_uvar(U)
    MG_LEN = 24
    MG_PTR = 0x1f24b40 "\260(=\252\254\177\0\0\20==\252\254\177\0\0\0j
+\372\1\0\0\0\0"
[download]

As you can see in section 2, the product reverted to 308 going back to the IV value. The same thing happened on 5.20.1. The flags changed a little, but the results were the same.

I've submitted a report on this to bug-Tk at rt.cpan.org