With no response for two hours, I decided that I might as well post both.
...I mean, if it comes to that, I'll delete the other one, right?
As I've mentioned, one of the coins is medieval... or, well, kind of medieval. Pre-1600, anyway.

This little piece over there is a pulo of Tver - or, at least, that's what it says.
However, this type was issued during the reign of Ivan the Terrible, when Tver was no longer independent; as such, Numista lists
the type under "Grand Principality of Moscow".
...Come to think of it, I'm not sure if anyone ever officially demonetized the pulos. They probably just slowly went out of use as they were no longer a useful denomination of currency.
Anyway, a pulo is 1/60 of a denga. A denga is 1/2 of a kopek. A kopek is 1/100 of a ruble.
That makes a pulo worth 1/12000 of a ruble (and yes, rubles were already a thing back then, though ruble
coins weren't).
That is to say, 1/12000 of the pre-1917 ruble. Then things went a bit wild for a while...
1922: 1 new ruble = 10000 old rubles
1923: 1 new ruble (1923) = 100 rubles of 1922 = 1,000,000 old rubles
1924: 1 gold ruble = 50000 rubles of 1923 = 50,000,000,000 pre-1917 rubles (5*10^10)
Two further redenominations, in 1947 and 1961, made one Russian ruble as of 1993 worth 100 "gold" rubles of 1924, or 5,000,000,000,000 (5*10^12) pre-1917 rubles.
Finally, a redenomination in 1998 took off three more zeroes, for a total of 5,000,000,000,000,000 (5*10^15) pre-1917 rubles per modern ruble, or 60,000,000,000,000,000,000 (6*10^19) pulos per modern ruble.
Multiplying that by the current rate gives a final answer of about 3.88*10^21 (that's 3,880,000,000,000,000,000,000) pulos per dollar; in other words, combining all the exchange rates, a pulo is worth about 0.000000000000000000000277 US dollars.
(I
think I didn't miscount the zeroes here; I'm not actually sure.)
You might be wondering how did I manage to find a coin whose lack of value above seem insignificant.
(Or, um, huge, I guess. Not sure how it works.)
However - though it might be a bit of an obscure fact - the Zimbabwean dollars
do not, in fact, hold the record for the largest banknote denominations ever.
That title goes to the Hungarian pengo in 1946, which reached denominations as high as 10^20 pengo (that's 100,000,000,000,000,000,000; the next level up, 10^21, was printed but didn't make it to circulation).
And the coin I'm about to show is a little bit older than 1946...
(...Actually, I'm cheating a bit in the below description; you would probably easily be able to figure out how. The non-cheating version gives
a lot less zeroes in the value, though.)

This piece here, a 2 filler 1898, is 1/50 of the (then Austro-)Hungarian korona.
The korona had received quite a bit of hyperinflation, in 1924, it was replaced by the pengo, at the rate of 1 pengo to 12500 korona.
Some fairly calm years followed, when even
silver coins were issued for the pengo; then came 1945, and things got a little bumpy.
Quickly summarizing: the last denomination to be issue for the pengo was the 10^20 (100,000,000,000,000,000,000) pengo, at which point the pengo was entirely replaced by the adopengo - at floating rates that eventually stabilized as 2*10^21 (2,000,000,000,000,000,000,000) pengo for 1 adopengo.
Then the adopengo in turn experienced some residual hyperinflation, and was exchanged at 200,000,000 adopengo to 1 forint; this is sometimes quoted as 4*10^29
pengo to the forint, which is technically correct but not
quite right - there were nowhere near as much pengo in the whole of Hungary.
(That is to say, 400,000,000,000,000,000,000,000,000,000 pengo to 1 forint. I almost stumbled at the zeroes even with the separators.)
The forint remains the currency of Hungary today; multiplying all the rates, we get 5*10^33 koronas per forint (I'm not writing
that out), or 2.5*10^35 of those 2-filler pieces from 1898 per modern forint.
That's per
forint; a forint isn't worth very much any more. One dollar is 306.57 forints, so the total rate comes out to... mini-drumroll...
7.66425*10^37 per dollar.
Or, in digits, just this once:
76,642,500,000,000,000,000,000,000,000,000,000,000.
The other way around, it comes to 1.30476*10^-38 dollars.
...I'm about to write
that out, right?
...OK. I apologize in advance.
For the record, it's 0.000000000000000000000000000000000000013 dollars (I've rounded it a bit, because at that point it doesn't really matter).