A dash, like a semicolon, can be used to separate a new thought in a sentence from the original thought. Let's take a look at our answer choices and see which fits this description the best...
1. "I am learning about Japan -- believe it or not, it is a chain of around 4,000 islands."
This looks pretty good. The speaker is representing an original thought in the part regarding their learning about Japan, and then introducing a new thought with the statement about the fact that Japan is a chain of around 4,000 islands.
This looks like a good bet as our right answer, but let us examine the other answers anyway.
2. "I am learning -- about Japan believe it or not, it is a chain of around 4,000 islands."
This choice doesn't seem to make much sense no matter which way you look at it. Grammatical and punctuation errors abound. We can scratch this off our list.
3. "I am learning about Japan believe it or not -- it is a chain of around 4,000 islands."
This would almost be correct if it had a period after the word 'Japan', since there is an interjection being used there. Commas will always precede an interjection (or follow one if it is at the beginning of the sentence).
So our correct answer is choice 1, as this is the only sentence that correctly uses the dash, as well as all the other punctuation.
Hope that helped! =)
