WASHINGTON — More women are getting the word that they may have breasts too dense for mammograms to give a good picture. What is not so clear is what to make of that information.

This summer, New York became the fourth state to require that women be told if they have dense breasts when they get the results of a mammogram. That is because women whose breast tissue is very dense have a greater risk of developing breast cancer than women whose breasts contain more fatty tissue. Plus, it can be harder for mammograms to spot a possible tumor.