rand returns a random¹, uniformly distributed number. To quote the documents, "Returns a random fractional number greater than or equal to 0 and less than the value of EXPR. (EXPR should be positive.) If EXPR is omitted, the value 1 is used. Currently EXPR with the value 0 is also special-cased as 1 - this has not been documented before perl 5.8.0 and is subject to change in future versions of perl."

So, if you pass 0 to rand(), it currently returns a value, x|0 ≤ x < 1. I believe it does the same think if you pass undef to rand, but RTFM². How you handle your value of number (incidentally,

$my number = 10;
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is not valid; I'm guessing you meant to write:

my $number = 10;
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but I'm sure you noticed the error message from perl!) depends on what you want to do. Possibly, something like

$value = $user_input or 10;
$x = rand($value);
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may suffice, but I think that it most likely won't.

Now, if you want to guarantee that rand always returns the same sequence of values, you've got to explicitly seed it, using srand. Once.

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¹Pedantically, they're likely not truly random; they're almost certainly pseudo-random.

²The manual is definitely a worthwhile read, too. As an old connoisseur of computing documents, Perl's is definitely deserving of accolades.