Unemployment rate drops to 7.8% on lower than expected job creation number?

The govt says unemployment dropped from 8.2-7.8% in one month, which is a great performance.

1. It takes over 150,000 new jobs per month to stay even with population growth
2. If unemployment dropped, we either have to exceed that number or the workforce has to shrink
3. The govt says the workforce grew!
4. But the government said the total number of jobs employed surged by 873,000, the highest one-month jump in 29 years. The total of unemployed people tumbled by 456,000.
5. Last month saw 142,000 new jobs as the rate dropped from 8.3 percent in July.

 There are now 325,000 more jobs than when Obama took office. That’s about 8,000 new jobs a month growth. See #1 above.

Can anyone explain this to me?

I must be stupid, but it seems internally inconsistent.