Yes. A standard deviation can be any positive value. If you divide it by the mean you should get a fraction every time. For example, if the mean population of a group of towns was 10,000 people, the mean and standard deviation would imply quite a modest variation: 10,000±937.5. But if you check the SD against the mean and you don’t get a fraction you have made a mistake (for example, you may accidentally have calculated the variance which is the square of the SD).