and the drop would have been even less (i.e. the unemployment rate would be even higher) if the labor force participation rate had not dropped by 0.3 percentage points as it did in September.
https://data.bls.gov/timeseries/LNS11300000

695,000 people left the labor force in September and are not counted in the unemployment rate.
http://data.bls.gov/timeseries/LNS11000000?output_view=net_1mth

I'm not surprised that the unemployment rate skyrocketed when the economy was locked down by government mandate, and that the UR rapidly dropped when the economy was opened up for the most part again.

The real test is how long will it take for the UR to get back to the 4.7% level that it was in January 2017 when Obama left office, a level that is 3.2 percentage points lower than it is now at 7.9%. (or back down even further to the February 2020 3.5% UR). I knew the economy would snap back to 80% or 90% of its former level, the worry is how long it takes -- how many years? to get back to 100% of where it was.

In January 2017, when Obama left office, the employment to population ratio was 59.9%. It's now 56.6%, a 3.3 percentage point drop. It has improved only 5.3 percentage points from it's low point in April (but it is up only 2.0 percentage points from 3 months ago and up only 0.1 percentage points over last month) (Edited to correct big errors in the last sentence)
https://data.bls.gov/timeseries/LNS12300000