When using quotation marks, you should always start with double quotations marks (e.g.,
"like these"). If quotation marks are then required within that quotation, you should use single quotation marks.
Examples:
Anne asked: "Are you really going to see 'Phantom of the Opera'?"
The articles states: "A giant squid may have attacked the 'Marie Celeste' as the
crew celebrated on the deck."

singles
within doubles - correct
(magazine article)
The Defence Secretary stood up and declared: "At 0600 hours tomorrow, "Ark
Royal" will set sail with her full compliment of crew."
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DON'T WORRY
This is not a hard and fast rule. In fact, several grammar books recommend that doubles be used within singles. For example:
Clapping slowly, Julian stood up and cried: 'That was even better
than your performance of "Twelfth Night" in London last year.'
Many writers prefer to use single quotation marks because they look less unwieldy.
The 'a' has fallen off the sign.
The "a" has fallen off the sign.
In summary, a writer can use doubles or singles in the first instance. However, whichever style is chosen, its use should be consistent throughout the document.
inconsistent use of singles and
doubles 
(magazine article)
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