davido has the correct answer but for a visual representation of his explanation, you could always use Devel::Peek ...

...
use Devel::Peek;

....

print Dump( $bottom );
my $middle = int(($bottom + $top) / 2);
print Dump( $bottom );

....
[download]

Enter the bottom most number: 1
Enter the top most number: 10
Hit enter once you have your number!
SV = PVMG(0x1009725b0) at 0x100847c98
  REFCNT = 1
  FLAGS = (PADMY,POK,pPOK)
  IV = 0
  NV = 0
  PV = 0x10020a3f0 "1\n"\0
  CUR = 2
  LEN = 16
SV = PVMG(0x1009725b0) at 0x100847c98
  REFCNT = 1
  FLAGS = (PADMY,IOK,POK,pIOK,pPOK)
  IV = 1
  NV = 0
  PV = 0x10020a3f0 "1\n"\0
  CUR = 2
  LEN = 16
Is it 5(l/h/t)?:
[download]

and from this, you can see no chomping has taken place but perl's DWIMery has taken your scalar (SV) and taken the string value (PV) and set its integer value (IV).