Let’s refer back to the sentence we looked at last week:
Tirelessly toiling on his project, as he believes that hard work ultimately pays off.
In addition, the line “as he believes that hard work ultimately pays off” is also a fragment because it begins with the subordinate conjunction “as”.
Subordinate conjunctions are words like as, although, even though, because, since, though, and whereas. If a clause begins with words such as these, it then becomes a subsidiary clause that functions to simply explain a main clause, but is unable to independently stand on its own. It also results in the clause ending on an abrupt and incomplete note.
Incorrect: As he believes that hard work ultimately pays off.
Correct: He believes that hard work ultimately pays off.
Rather than adding a main clause to complete the fragment, the above incorrect example could also stand on its own as a proper sentence if “as” were to be removed instead, as shown in the example above.
It is useful to note that the sheer length of words is not what determines what makes a sentence, but the presence of a subject and a verb, and a complete thought being formed as a result.