Мне нужно отнести заявление в отдел кадров до обеда.

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Breakdown of Мне нужно отнести заявление в отдел кадров до обеда.

• в: to
• обед: the lunch
• нужно: to need

Questions & Answers about Мне нужно отнести заявление в отдел кадров до обеда.

Why is it мне нужно, not я нужно?

Because нужно is used in an impersonal construction.

Russian does not say this the same way English says I need to.... Instead, it is closer to:

To me, it is necessary to...

So:

• мне = to me in the dative case
• нужно = necessary / needed
• infinitive = the action that needs to be done

That is why мне is correct here, not я.

A similar pattern appears in:

• Мне надо идти. = I need to go.
• Ему нужно позвонить. = He needs to call.

What exactly does нужно mean here?

Нужно means something like it is necessary, it is needed, or one needs to.

In this sentence, it combines with the infinitive отнести to express obligation or necessity:

• мне нужно отнести... = I need to take/deliver...

It is a very common everyday way to say that something has to be done.

A few related words:

• нужно = necessary, needed
• надо = also means need to / have to, often very similar in everyday speech
• должен / должна = must, am supposed to, more personal and direct

So мне нужно отнести заявление sounds natural and neutral.