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Although such meters are not highly accurate, it's rare for one to be
off by nearly an order of magnitude.

I hope it's not a case of misreading the part values. An OLD capacitor
that says 390 on it, such as you might find in your junkbox, might be
a 390pF capacitor, except that they would have called it 390uuF
(micromicrofarads) in the day. But a NEW capacitor that is labeled 390
is a 39pF capacitor; the final digit is a multiplier, and the 0 says
to add no zeroes to the end.

For whatever reason, nanofarads never caught on the US though they are
used elsewhere. On this side of the pond the common bypass capacitor
is 0.1uF, but a British builder might call it 100nF instead. Values of
1000pF up to just shy of 1uF are usually given as fractional
microfarad values, so other popular bypass values are .001uf (1nF) and
.01uF (10nF). Similarly we don't use millifarads, so a really big
capacitor might be 10,000uF rather than 10mF. You don't see full
farads used until you get up into supercapacitor territory, so that
10mF part would NOT be referred to as 0.01F, but a 470mF
supercapacitor would be identified as 0.47F.