American style (Chicago, APA, and MLA) specifies that a period goes inside the quotations.

British style, on the other hand, specifies that a period goes outside the quotations.

http://blog.apastyle.org/apastyle/2011/08/punctuating-around...

As I recall, according to "Strunk and White", and the "Chicago Manual of Style", all punctuation is supposed to be included inside the quote characters.

I happen to disagree with them, but they have been considered authorities on the proper way to write in the English language for many decades.