***** NOT A TEACHER *****
(1) Excellent question. Until a teacher answers you and me, may I offer a few
(a) I believe that "deciding to leave" is called a participial phrase (or "clause"
in some books).
(i) As you can see, it is attached to "I." That is, it modifies "I."
(2) In your language, are there many ways to express an idea? Well, so are there
(3) I think that the idea in your sentence could be expressed in these ways:
I decided to leave. I packed my clothes and left a note to say that I had gone.
Because I had decided to leave, I packed my clothes and left a note to say that I had gone. (adverbial clause "because I had decided to leave.")
Deciding to leave, I packed my clothes and left a note to say that I had gone.
As you can see, the third sentence is shorter and expresses your idea faster.
Of course, I think that this kind of sentence is usually limited to writing. It would
sound kind of funny if your conversation were filled with this kind of construction
Careful! If you decide to use this kind of construction (in writing!), do not make the
mistake that many learners (and native speakers) make. Always make sure that
the person who is doing something is clear to the reader.
Here is a humorous example from The Grammar Book (by Mesdames Celce-Murcia
Following the recipe, my cake was a great success.
This sentence says that my cake followed the recipe. Of course, a cake cannot
follow a recipe. I am the one who followed the recipe. So this would have to be
rewritten something like this (the following is only my sentence):
Following the recipe, I made a cake that was a great success.
(Do you notice that "following the recipe" is attached to "I"? In other words:
I followed the recipe. I made a cake that was a great success.
Because I followed the recipe, I made a cake that was a great success.
(In writing only!) Following the recipe, I made a cake ....)