I have a list which will store Number objects. The list will be populated by parsing a list of strings, where each string may represent any subclass of Number.
Number cannot be instantiated because it is an abstract class. I would recommend passing in Numbers, but if you are set on Strings you can parse them using any of the subclasses,
Number num = Integer.parseInt(myString);
or
Number num = NumberFormat.getInstance().parse(myNumber);