I have data in an Excel spreadsheet with values like this:
The cells are formatted as Percentage, and set to disp
The BIFF formats are an open specification by Microsoft. (Note, that I say specification not standard). Give a read to this to get an idea of what is going on.
Then those BIFF you see correspond to the some Excel formats. BIFF5 is XLS from Excel 5.0 and 95, BIFF8 is XLS from Excel 97 to 2003, BIFF12 is XLSB from Excel 2003, note that Excel 2007 can also produce them (I guess Excel 2010 too). There is some documentation here and also here (From OpenOffice) that may help you make sense of the binary there...
Anyways, there is some work has been done in past to parse this documents in C++, Java, VB and for your taste in C#. For example this BIFF12 Reader, the project NExcel, and ExcelLibrary to cite a few.
In particular NExcel will let you pass an stream which you can create from the clipboard data and then query NExcel to get the data. If you are going to take the source code then I think ExcelLibrary is much more readable.
You can get the stream like this:
var dataobject = System.Windows.Forms.Clipboard.GetDataObject();
var stream = (System.IO.Stream)dataobject.GetData(format);
And read form the stream with NExcel would be something like this:
var wb = getWorkbook(stream);
var sheet = wb.Sheets[0];
var somedata = sheet.getCell(0, 0).Contents;
I guess the actual Office libraries from Microsoft would work too.
I know this is not the whole tale, please share how is it going. Will try it if I get a chance.