What type of sentence is without stoping to think?

The phrase "without stopping to think" is not a complete sentence. It's a prepositional phrase functioning as an adverbial modifier.

Here's why:

* Missing subject and verb: It lacks a subject (who is doing the action) and a verb (the action itself).

* Modifies a verb: It describes how an action is performed. For example: "He ran without stopping to think."

To make it a sentence, you need to add a subject and a verb:

* He ran without stopping to think.

* She jumped into the water without stopping to think.