It is certainly possible to create an exactly fixed quantity of money. Since money is now mostly created electronically the central banks could simply decide to freeze the quantity. Bills and coins could be replaced with paycards.
This still wouldn't mean that some countries could exploit other countries through free trade. Yes, countries with faster growth would get more of the worlds money. No, this is not exploitation, this simply reflects that they produce more.
The amount of gold could have been divided into arbitrarily small parts if bills were used to represent a certain amount of gold. The reason that the gold standard was discarded was the same reason as countless time before in history: The government wanted more money than it had available. Some of the consequences:
http://www.prudentbear.com/archive_comm_article.asp?category=Guest+Commentary&content_idx=27975
The true inflation, unemployment and deficit numbers:
http://www.gillespieresearch.com/cgi-bin/s/article/id=264
http://www.gillespieresearch.com/cgi-bin/s/article/id=278
http://www.gillespieresearch.com/cgi-bin/s/article/id=300