What is means: According to Merriam-Wesbter online, importunate means "troublesomely urgent: overly persistant in request or demand." The sentence provided states "Sylvia was becoming fed up with the importunate phone calls she continued to receive from charities seeking donations."
Level of Familiarity: I have heard this word before, but like many other words, I needed to be reminded of the words exact meaning.
Do I Want to Know This Word Well and Why? I kind of like this word. I think it is a good word to use in conversation. I mean, look at how the word is used in the sentence above. I love it and it makes Sylvia seem very irrated, and the calls even more obnoxious. I think I am in love with this word!! Just kidding about that but I think this word is another one of my million dollar words (or is it one hundred).
Do I Think Others Should Know This Word Well...if so WHO and WHY?: Of course! Personally, I think this is a good word to use. Think of all the things or people in your life that you could use this word for. It is a good word to describe.

