If someone asks you about your ex there is nothing wrong with telling them you broke up. Always remember that life is a "personal journey". You get to set YOUR own rules!
Most people have dated more than one person in their life and therefore they understand that "breakups" are just as natural as dating. It happens all the time. There's nothing to be ashamed of. Having said that I "personally" feel pretending to still be in a relationship around my closest friends and family is lying. People who are close to you usually want to lend you support during the rough times. Sometimes when people keep painful things to themself they begin to believe they are "all alone" which leads to deeper depression and sometimes suicidal thoughts.
So whenever you feel comfortable to let people know that is when you should do it.