That's a nice experiment. I tried a quick test with my 'scope. I grabbed the nearest ceramic 10nf capacitor - as Spehro suggested, it was marked "103":
simulate this circuit – Schematic created using CircuitLab
Time to discharge C1 from 9.12V to 4.56V was measured at 70 milliseconds.
SW1 was done by simply stabbing the top capacitor lead at the DC supply's positive terminal.
I've not done an error analysis because the capacitor tolerance is unknown and my measurement was quickly "eyeballed". The calculated result of R1 was close-enough to 10^7 ohms.