There could be a few different answers for this question.
If you consider the birthdate of the country to be the date it declared independence from its colonial power then I'm 9.923% of the age of USA.
If you consider the birthdate of the country to be the date it signed the treaty granting it independence from its colonial power then I'm 10.227% the age of USA.
If you consider the birthdate of the country to be the date the treaty granting it independence from its colonial power became effective then I'm 10.257% of the age of USA.
This question would be harder for people from older countries to answer since there's not an exact date or year their country began that they know about.