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When you tell someone something that you heard from other one, you may say "I hear that __", or "They say that __", or "There is a rumor that __".

「___[なん]だって(さ)。」is just same as those.

You can use 「 ___らしい(よ)。」 too.

Those are used when the rumor is not known yet by person who you are just telling.

For example.

They say it'll become rain. You didn't know it, do you?

「あめが ふるん だってさ。しらなかった でしょう？」

If the rumor has already known by person who you are just telling

or the rumor is about the person who you are just telling,

You use 「___[なん]だって(ね)。」 or 「___らしい(ね)。」.

For example.

They say it'll become rain. You knew it, didn't you?

「あめが ふるん だってね。しってた でしょう？」

I hear that you went to Japan last year. Is that right?

「きょねん にほんに いったん だってね。ほんとう？」

Addition.

なん is used when the sentence ends at nouns or na-adjectives.

かれはがくせい + なんだって

He is a student(noun) + I hear

Datte itself means prettymuch "However/But". Nandatte is like "Why?!"

In those examples, it's like "But why!" or "What on earth!"