Perceptiveness is the quality of being perceptive: how good someone is at noticing small things and understanding people or situations. Her perceptiveness made her a wonderful friend — she always knew when something was wrong. You will mostly meet this word in writing. In talk, people more often say “she is so perceptive” rather than “her perceptiveness.” Used of a person, it is a compliment. It is not a common classroom word; “insight” or simply “she notices a lot” will often do the same job in easier English.