Her students looked at her in surprise. Curious, she drew closer and found that the students were listening to a new rock hit.

When I first saw 'Curious' at the begining of the second sentence, I didn't understand how an adjective can stand separately.

Q1) Now I think something must be omitted, mustn't it?(Is this correct tag questionEmotion: smile?)

Q2) Is being omitted in front of 'curious?'

Q3) And when they are put in full formal, are they 'Because/as I was curious, she drew~?'
Dear Moon

I think your "Q3" is about right. I cannot give you the exact rules but, in English, if your sentence is dealing mainly with the question "Why?" then you can leave out the "Because" clause and replace it with an adjective or adjectival phrase at the beginning of the sentence. Here are some examples..

- Why did she draw closer to the students who had looked at her in surprise? [Question in your mind]

- Because she was curious, she drew closer to the students [Long answer, with because]

- Curious, she drew closer to the students [Acceptable short sentence]

- Why does that building seem more modern now?

- Because it has been painted green, the building seems more modern

- Painted green, the building seems more modern

- Why did Alfred give the beggar money?

- Because he is always generous, Alfred gave five pounds to the beggar

- Generous as ever, Alfred gave five pounds to the beggar

- Why did we not see the beetle?

- Because the beetle is green, we did not notice it against the leaves of the tree

- Being green, the beetle could not be seen against the leaves of the tree

Hope this may help, Dave
Wow,, this is awesome..

I didn't know omitting 'Because ~' sounds more modern. It's good to know.

Then, how does this omition apply in speaking and writing?; does it make the sentences sound formal or informal?

One more question, if I say 'having painted green~,' and not 'painted green' in your example, does 'having' imply the tense of the original sentence is the past perfect? (Because it had been painted green, the building seemed more modern.)
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Dear Moon

As said, I'm not sure of the exact rules, but the general idea of missing out the "Why / Because" of a sentence works in many areas of English..

Informal

- Bought a new car! - you must be short of money now

[= Because you bought a new car, I guess you have no money left now]

- Saw John yesterday: wearing a new suit, he looked a whole lot smarter!

[= Because he was wearing a new suit, he looked a lot smarter]

Ordinary

- Needing a pint of milk, he went to the shop

[= Because he needed a pint of milk, he went to the shop]

- Cold and weary, he stopped and made a fire

Formal

This refers to your question about "having". I believe the usage is related, technically, to the Latin gerundive (other teachers will have to help out here!). But this means that many speakers would recognise it as a formal and proper usage..

- Having commited our funds to the New York shop, we had to cut back on advertising

[= Because we were using our money to start up the New York shop, we had to spend less on advertising]

In some areas of English, you do need to be careful to match verb tenses, buI don't think there is a strong rule here - the tenses can work in different ways to give different meanings..

- Painted green, the building seemed more modern

[= that was what I felt about the bulding at the time]

- Painted green, the building seems more modern

[= if you go and look, you will see what I mean]

- Painted green, the building had seemed more modern

[= but now they have repainted it and it looks old-fashioned]

The following also seem OK to me..

- Having been painted green, the building seemed more modern

- Having been painted green, the building seems more modern

I don't think the last sentence is wrong, but I would probably just say -

- Now that it's painted green, the building seems more modern

Best regards, Dave
Ah.. I find a synonymous expression 'now that' for 'because' in this pattern.

I got a clear idea from your in-depth analysis..

I seems I find new stuffs by asking here even if I think I know about something a lot.

It's very glad to see a nice helper like you.

Thank you very much.