Reading fixed doubles with fixed point from file and convert into long

I am reading US Dollar prices from a file. Example

asset_jsld 40.54
asset_sxd 40.80

I want to have a map that has these prices as a key. Since float or double are less than ideals keys, I am converting my values into Dollar Cents and I am storing them as a long. words is a list of string by column of the original file.

using boost::spirit::qi::parse;
// ...
if (!parse(words[1].begin(), words[4].end(), double_, price_d))
  // Error handeling
long price = boost::numeric_cast<long>(price_d * 100.0);

The problem is that the double is 40.80 and the long is 4079. Does this rounding error come from numeric_cast? Is there are numerical stable alternative?