what is actually stored in $a[$i]? Is it the string "123" or the number 123.0?

split returns strings.

And does it make any difference to the perl programmer?

No. It works as intended in practically all cases.

The only time I can think of where it makes a difference is when you use |, & or ^ on it with a string as the other operand.

>perl -le"($x,$y)=map 0+$_,  @ARGV; print $x|$y;" 2 8
10

>perl -le"($x,$y)=map ''.$_, @ARGV; print $x|$y;" 2 8
:
[download]

I'm using the results entirely in numerical calculations, so I want to do all conversion of string-to-number (if any) at the time I read the file and get it over with early.

It's not needed, but you could use

my @nums = map 0+$_, split /,/;
[download]

I've been using the perl debugger to print these variables but I can't (yet) tell whether it's printing a string or a number.

That just shows you how much it matters.

Devel::Peek will show you. pPOK = string, pIOK, pUOK or pNOK = number. Can be both.

>perl -e"use Devel::Peek; my $x=123; Dump($x);"
SV = IV(0x1826628) at 0x225350
  REFCNT = 1
  FLAGS = (PADBUSY,PADMY,IOK,pIOK)           <-- signed int
  IV = 123

>perl -e"use Devel::Peek; my $x='123'; Dump($x);"
SV = PV(0x226154) at 0x225350
  REFCNT = 1
  FLAGS = (PADBUSY,PADMY,POK,pPOK)           <-- string
  PV = 0x18227c4 "123"\0
  CUR = 3
  LEN = 4

>perl -e"use Devel::Peek; my $x=123; qq{$x}; Dump($x);"
SV = PVIV(0x22718c) at 0x225358
  REFCNT = 1
  FLAGS = (PADBUSY,PADMY,IOK,POK,pIOK,pPOK)  <-- signed int AND string
  IV = 123
  PV = 0x18227cc "123"\0
  CUR = 3
  LEN = 4
[download]