Can someone check my math?

I came across this quote from an Ohio State website with notes from a lecture.

The impact of human activity (industrial or otherwise) upon the Earth's atmosphere is real and it is measurable.

Which really rubs me the wrong way, because the literature I've read, from wikipedia to peer reviewed original research, has vastly different conclusions about the exact measurable amount of human control over climate, what is a correct method for conducting those measurements, and assigning meaningful amounts of the blame to natural forces.

But what the hell, lets do some science.  Total atmospheric mass is 5.1480×10¹⁸ kg, at least according to Wikipedia.  The AGW proponents claim that around 20 Giga Tons of Carbon are put into the air every year (some claim 29 gigatons, but I like round numbers as starting points).  At this point the math is simple.  Convert giggatonnes to kilograms, and for the sake of easy math I'm going to assume metric tons, so 20 gigatonnes becomes 20,000,000,000,000,000 kg.  To make the math easier we'll just knock off sixteen zeros (divide each side of the equation by 10 quadrillion), so we get 2 kg divided by 514,800 kg.  That gives us 3.855 times 10 to the negative 6 power of carbon as a percentage of the total atmosphere.

But wait, there's more!  There is always more isn't there?  So we've done a back of the napkin calculation here and shown how little 20 giga tons of carbon actually is in relation to the atmosphere.  But this calculation exists without a time stamp, so lets multiply our answer by a century and see what the cumulative affect is.  But we are stuck down at 3.855 times ten to the negative 3 power.  Still a very very small number.

Multiply that original number by a thousand and we are still at 3.855 percent of atmosphere by weight. Just so you know, that is the current level of emission (roughly) along a ten thousand year time span.

But wait again!  Don't we measure CO2 in "Parts Per Million" instead of a percentage of total mass?  Why yes, yes we do.  Here the math gets a little more complicated as different molecules have different masses.  But we can pull out Avagadro's Number and crunch it, or we can consult a handy reference tool http://www.engineeringtoolbox.com/molecular-mass-air-d_679.html and look up a standard molecular weight for "air".  So 28.97 kg per mol, then 1 kg of air has 1/28.97 mols of "air" in it.  So we get 0.03451 mols of "air" per kg of "air" and multiply that by 6.022x10 to the 23rd power will give us the number of molecules in that kg.  So we are looking at 2.078 times 10 to the 22nd power molecules per kg of air.

So, to calculate the number of molecules of anthropogenic carbon in that kg we need to multiply the percentage of carbon by the total the total number of molecules.  So 3.855 times ten to the negative 6 power multiplied by by 2.078 times ten to the 22nd.   That gives us 8.073 times ten to the 17 molecules of carbon.  Now to get that back into a useable percentage form to calculate parts per million we divide 8.077 to the 17th by 2.078 to the 22nd.  Simplifying the math that is 8.077 divided by 2.078 to the 5th.  That gives us 3.885 to the negative 5th.  Or 0.00003885 which is about right I think, as 1 part per million is equal to 0.0001, so at this rate we should expect atmospheric CO2 to gain 1 part per million about every two and a half years.

Does that fit with our CO2 measurements?  No, because even AGW proponents say that 60% of anthropogenic CO2 is taken back by the carbon sinks, it is only the remaining 40% that sticks around.  So what that means is that we can expect less than 2 ppm increase in CO2 per decade if my math is correct.  I have very little confidence that my math is correct because this is really just my scribbling on the back of a digital envelope.  So all that talk of catastrophe if we don't cut carbon emissions now?  Not too worried about it, at 2 ppm per decade it would take (lets see that's 20 ppm per century, doubling would require 400 ppm) about 2,000 years.  If you increase my starting estimate to 30 gigatons you increase the incoming carbon by 50%, which means that this final number to double carbon content of the atmosphere only goes down to 1,000 years (assuming the rest of the math is solid).

Seriously, can anyone check my math?