mifflin,
looks_like_number was introduced in version 1.10 of Scalar::Util. The sub looks like this:

sub looks_like_number {
  local $_ = shift;

  # checks from perlfaq4
  return 1 unless defined;
  return 1 if (/^[+-]?\d+$/); # is a +/- integer
  return 1 if (/^([+-]?)(?=\d|\.\d)\d*(\.\d*)?([Ee]([+-]?\d+))?$/); # 
+a C float
  return 1 if ($] >= 5.008 and /^(Inf(inity)?|NaN)$/i) or ($] >= 5.006
+001 and /^Inf$/i);

  0;
}
[download]

As I stated in my reply - I do not think this meets your requirements because it also handles decimals, scientific notation, NaN, and Inf.

Cheers - L~R