All the same rules apply to single quotation marks. So when you have a single quote mark followed by a double, that doesn’t change where the period goes. It goes inside all the quote marks.

Rules for Placement of Puncuation Marks with Quotations Periods and commas are always placed inside quotation marks. Ex: In "The Lottery," Tessie Hutchinson protests, "It isn't fair." Exception: In ...

The Rules First, let's address single quotation marks. One rule covers this: Use single quotation marks instead of the standard double quotations within another quoted phrase.

Do not place in quotation marks: names of newspapers, magazines, central texts of a religion (Bible, Koran), dictionaries, handbooks and reference books. Names of concertos, operas, overtures, sonatas ...

In an age where almost everyone’s a writer and a self-publisher, people guess at how to punctuate terms in quotation marks. Naturally, no one guesses that punctuation rules might not be logical.