This is why I write slower than I'd want to · 7:58pm Mar 28th, 2016
From the notes on one of my fics:
[One cubic metre of gold] weighs 19.282 kg. Assuming that one bit is made of pure gold and is the size of a modern $1 coin (26.5 mm in diameter, 2 mm thick), its volume is 1103,09 cubic milimetres, that is 110.309 cubic centimetres or 0.000110309 cubic metres. So a cubic metre of 1 bit coins is about 9065 bits. Of course, if bits were to be made of pure gold they'd have to be smaller: a golden coin of that size would weigh 2.13 kg and would be worth $83,574.32 each.
Well, let's hope their coins are smaller/ have higher denominations. Though we've seen ponies using gems as currency and for a good reason: a cubic centimetre of gold weighs 19.3 g (silver is only a bit more handy at 10.49 g), but the same amount of rubies or sapphires weighs from 3.95 to 4.1 g, diamonds – 3.52 g, and emeralds – up to 2.8 g. If you want to pay someone 10k bits for a new cart, you'd better have some gems...
On a side note, remember how in The Goblet of Fire that muggle dude described galleons as "golden coins the size of hubcaps"? Well, JKR was never good with numbers...
Actually, I think you did the math there wrong. The volume of the bit would be πR² * h. That'd be 3.14*0.0265*0.0265*0.002, or 0,00000441013. That, in turn would mean 85g of gold (85.04 rounded), that in turn is worth $3,343.05 as of today ($39.33 to the gram).
Engineering is something you carry in your soul
That being said, yeah, research is rather time consuming, but crucial to good writing. Keep up the fight!
So I wasn't the only one to find the reasoning here kind of weird.
You just had to cross the mass of one bit with with the gold and you had the volume and value of gold.
Well like @Neece said you had the volume wrong anyway.
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26.5 mm is the coin's diameter. R in here is radius, which is 13.25 mm. So, (13.25^2)*3.14 = 551.26 square mm (circle area). 551.26*2 gives 1102.53 cubic milimetres (still slightly different from 1103.09 I got initially, but I guess I rounded it up differently this time).
The mistake is that 1103.09 cubic millimeters is 1.10309 cubic centimeters, not 110.309. Everything after that part is off by a factor of 100.