Carrying A Couple of Grams of Uranium in Pocket - Was it Dangerous? In short:  I handled a small amount of uranium when I was young and kept it next to me in a bottle for years.  Should I be concerned?
The background is that when I was a young (10-ish), I was growing crystals and doing other chemical experiments.  To help me, my Dad procured from his work several little plastic bottles of chemicals, given to him by one of the chemists where he worked. (This was in the 1960s - things were different back then!) One bottle was labelled as a salt of Uranium. I cannot quite remember the salt but I think it was labelled something like U(Ac)n - sorry I could not do the subscript ; I cannot remember what the n was. It was a yellow powder.  I only used a little of the uranium and kept the rest in my room.  Later, age 18, I told my chemistry teacher I had some uranium and he would not believe me, so I brought it to school.  The teacher put it next to a geiger counter which registered a lot of activity and my teacher was shocked and said I ought not to have been carrying it around in my pocket.  Neither he nor I knew what ion Ac was supposed to be - we assumed the chemist was using some shorthand of his own.  So how much radiation was I exposed to?  The bottle contained about two milliliters (so I suppose there was a couple of grams) and was within ten feet of me for 12 hours a day for 8 years or so and for a couple of days it was in my pocket and I must have handled it with my bare hands a couple of times.  I seem to be very healthy.  Should I be worried?
 A: The compound in question is likely to be uranyl acetate (or at least was labelled as such: "Ac" is chemical shorthand for acetate).
Uranium salts were mainly used, prior to the nuclear age, as glazing agents in pottery and ceramics because of their fluoresence. This in itself shows they are relatively innocuous.
Most uranium isotopes have very long half-lives and are only mildly radioactive. The uranium Wiki entry e.g. shows a person holding a slab of uranium metal, protected by no more than a pair of rubber gloves.
The major danger of uranium to human health comes from potential ingestion or inhalation of uranium bearing powders: very intimate contact of human tissue with solid uranium containing particles exposes cells to radiation. 
The way you describe storing the material makes me think you probably don't have much to worry about.
A: There is the case of David Hahn. As a youth he became obsessed with making nuclear reactors. He cannibalized americium from smoke detectors and played around with large amounts of radioactive material. He died recently at age 39, and it appears he suffered from long term exposure to radiation. Taylor Wilson is a younger "atomic kid," now age 21 or 22 or so, who has the amazing ability to get hold of these materials and fabricate nuclear devices. I am not sure what his radiation health status is. 
In high school I thought about tearing into smoke detectors to do these things, but concerns over radiation kept me from doing it. I also got more interested in high energy particle physics and black holes and the like. Nuclear reactors seemed in a way "old fashioned." 
The concern is heightened if you kept this uranyl acetate really close to you. If you carried it in your pocket all the time then I would be concerned. If it was on a shelf or cabinet and most of the time you were say $10$ feet away from it then I would be not so concerned. The main problem is $\gamma$-radiation and it falls off in intensity as $1/r^2$ as do all photons. If you kept it in your pocket you might also have genetic damage to germ cell lines; consider it being close to the testicles of a man or the ovaries of a woman. If kept at a distance, say as with americium in that smoke detector on your home ceiling, then there should be no problem.
