I understand your concern. I discovered high levels of radon in my house after I bought it. It wasn't a pleasant feeling building up while reading about the dangers. Here is what i did (this is the same answer I gave to another guy asking here). And yes I fully understand since I have small children:
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I had a very similar problem with radon gas in my basement. It is indeed dangerous for your health. The concentration is not measured in percentages (that would be huge and lethal). It is measured in Bq/m3 or in pCi/l. You can find more information here:
http://radon-solution.com/
I investigated the problem and then I implemented a solution like the one described here:
http://handyowner.com/2008/08/17/installing-a-fan-based-radon-mitigation-system/
I did all the work myself and from 8 pCi/l now I got to 0.4 pCi/l. And all for about $350. The price includes
- the fan
- the electronic detector for continuous monitoring (I ordered them online from the first site)
- the equipment rental from Home Depot (drill and bit to put a hole in the concrete slab in the basement)
- pipes
Read about it and act. If you don't feel comfortable doing the work yourself there are lots of contractors who can (for a price of course).
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Good luck!