If working with all those leading zeroes gets a bit confusing, the formula can be further broken down thusly:
1,000,000 / (2*pi) = 159,155
this allows you to use microfarads instead of farads.
so, the -3 dB LF point, with a 0.047 uF coupling cap would be
159,155 / (0.047uf X 470,000 ohms)
or
159,155 / 22,090
or
7.205 Hz OK, Mister Spock, let's not be so Vulcan logical, and act a bit more human)...
7 Hz is more than good enough, we're not splitting atome here
If you like to work with uf and K ohms, then it would work out thusly:
The formula can be further broken down one more time, to factor in K ohms: 1000 / (2 X Pi) = 159.155
159.155 / (0.047uF X 470K ohms) or 159.155 / 22.09 = 7.205 Hz
Old school trick, to determine PI to a ridiculously good figure, from the days of the primitive "four banger" calculators:
remember the number
113355
divide 355 by 113 = 3.1415929
Actual PI = 3.1415927
Of course, for our purposes, 22/7 is more than good enough: 3.142857
/ed B