My questions:

  1. How to use “ 难道 ” in Chinese sentences?

  2. What is the difference between 你不知道吗? and 你难道不知道吗?

  • 2. It means the asker feels surprised that you don't know what you should know. – Nighon Jun 29 '16 at 10:27
  • The meaning of "难道” could also indicate that the asker is angry. I would say the accurate meaning depends on the context. – Kai Jun 29 '16 at 10:41
  1. Grammatically, "难道" is an indication of 反问句(a rhetorical negative question). The exact correspondence in English may differ depending on the context, but I will give some examples here:

    (难道)你不知道吗?
    > Don't you know it? (I thought that you knew it.)
    你(难道)不知道……吗?
    > Don't you know that ......
    (难道)你不明白吗?
    > Don't you understand?

    这难道不是真理吗?
    > Ain't that the truth?

    (难道)你今天不用上班吗?
    > Don't you have to work today?

    你不来吗?
    > Aren't you coming?

Personally, I believe it's sometimes better to put 难道 in the beginning, though most of the time, the order doesn't matter in spoken language.

  1. Questioning with a negating particle 不(not) is a negative question itself. So basically they are the same in meaning.
    The possible difference is: in the second question with 难道, the speaker believes more firmly that the listener should have known (the object), to the extent that he is/would be very surprised if the listener doesn't know anything. This may also be implied in the first sentence without 难道, again, depending on the context.

Not a comprehensive answer, but:

难道 gives special emphasis to the question, like "Could it be that...?" and can be used to contrast with what was previously said, especially to expose some presumption or surprise (that could serve as an explanation for what has been said previously.

E.g.

你今晚不要和我们去游泳吗? 难道你不会游泳吗?

[usually, there would be some pause between the two sentences because the speaker needs some time to draw the concluding second sentence from the reaction or response of the other speaker]

"Aren't you joining us to go swimming tonight? Or perhaps could it be that you can't swim?"

(Not very elegant translation, but points out the meaning of 难道)

The difference between the two sentences you provide, should now be clear, the second one expresses the surprise over the reaction or response of the other person in a form of presumption/speculation (It's not necessary that the other person does not know [whatever it is], but we just make a guess). The first sentence is just a plain question with no speculative character.

  • I would say the tone is much stronger and more negative than "could it be that..." – NS.X. Jun 29 '16 at 18:39

难道 is used to express “can it be possible that…” or “maybe” with the subtext that “it should be” or “someone should”.

Sometime with an exaggerated tone.

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