The number 123321 contains more information than 3. This isn't true, or at least, it isn't true most relevant ways. Most obviously, if I need to specify which

The number 123321 contains more information than 3. This isn't true, or at least, it isn't true most relevant ways. Most obviously, if I need to specify which record in my database (of, say, a million records) is to be read, then "3" and "123321" contain precisely the same amount of information. But I think that even in more common cases: "how many birds are at the bird feeder?"; "how many gallons did it take to fill you gas tank?"; "what's you GPA?", the answer, regardless of its magnitude, conveys the same amount of information. Now, precision is a different story. "I'm going to take a couple of weeks vacation in July" contains less information than "I'm going to take 11 days of vacation in July". "My gas tank has a capacity of 16 gallons" contains less information than "my gas tank has a capacity of 15.9 gallons.".