How Large A Dose Of Radiation Is Given Off By The Average Cat Scan?

I once broke my leg and was given a CAT scan, even though a regular X-ray had revealed it to be a clean break. I was distraught on finding that the machine seemed to be on for five to ten minutes. Even one still picture seems to contain much more gamma radiation than would be taken in due to natural exposure by the body.
I later asked this question of an employee of a local synchrotron plant, which professes to specialize in concentrating beams of radiation so that they only hit a very tiny and minimal part of the body, thus doing less damage. The employee said he did not know because he was not a health care professional.
I would like to know the answer expressed in commonly used units of radiation.