In addition to all your other problems, you also face the fact that most fractions of a dollar will require infinitely repeating digit sequences in hexdecimal. For example, $13.01 is *$B.028F5C28F5C28F5C … * in base 16.
Whichever common notation you use for this, I think you’ll have trouble squeezing most amounts into that little box on the right side of a typical check. I’d certainly have that trouble on mine anyway.
No, that’s not really one of the problems. We have to round sometimes using decimal currency too. Wouldn’t you just round up to $B.03?
There is no law (AFAIK) on the subject. However, your contract with your bank probably spells out what types of checks it will permit you to write, and merchants can decide what kinds of checks they will accept.
Here is a fun article about what you are “allowed” to do with checks, and how your typical cashier will respond. The chart on the last page is a good start.
We do round in decimal currency, but that’s the last step before specifying the real amount of money to be paid. The actual amount of money that ever changes hands (between two American banks anyway) is always some whole number of cents, right? I thought?
Forget hexadecimal for a moment. Are we allowed to write checks for “$55 2/7” dollars, with the understanding that the actual amount it represents is $55.29? Seems iffy to me.
Here is a sample deposit account agreement.
Here are some relevant provisions:
Also, here is the UCC provision regarding instruments payable in foreign money, which is something that a few people have asked about:
I recently worked as a software developer on electronic check processing. This was the wisdom passed down to us from people who know about the banking industry:
Legally, what matters is the long-hand written amount field (the legal amount field). The numeric amount (the courtesy amount) need not be accurate, legible, or even present.
Practically, however, the legal amount field will almost always be ignored by the person who processes the check, unless there is something that raises a red flag in the rest of the check (the MICR line, or the courtesy amount).
So, if you use a hexadecimal number in the courtesy amount, all you are doing is forcing the poor teller, who processes dozens of checks per minute, to stop what he is doing and look at the legal amount.
If the legal amount is in hexadecimal, I’m not sure what the legal ramifications would be, but practically, the check is almost certainly going to get rejected as an illegible amount.
Again, if the courtesy amount is in decimal dollars, practically, it won’t matter what is in the legal amount unless there is a dispute.
Finally, the whole purpose of the courtesy amount is courtesy. It is a courtesy to anyone who would like to know the amount of the check at a glance. Writing it in hex defeats the purpose.
Holy smokes, I get to use my favorite math geek joke twice in one week!
Why do mathematicians get Halloween and Christmas confused?
Because OCT 31 = DEC 25.
Would the OP like to give me change for this $100 bill I’ll accept 160[dec] $1 bills.
Anyway, most money is either complex or imaginary these days.
NQR. As the UCC explains:
In other words, a check need not contain a handwritten amount. If it does, and then then words prevail over numbers, typewritten terms prevail over printed terms, and handwritten terms win over typewritten and printed terms. But see the linked above for how the folk-wisdom of cashiers and tellers has modified the law.
I have, in my business, accepted a check written in French for about $30,000 (it was actually in dollars, not Euro), and the bank cashed it with no problem. The amount was in decimal (although with the commas differently than the US) and the “spelled out” amount was in French. So at least some banks will deal with it.
Especially for their business accounts. 
Hex checks vex!
Una’s example just proves that bankers and proof operators pay no attention to the legal amount. AFAIK, the imaging systems ignore it as well - the new systems OCR the check and are looking for digits.
So the two likely results are:
A: Imaging system mis-reads $100h (silly intent to be $256.00d) as $100.00d. Big ruckus happens later when the banks are doing “inclearings” and trying to find the sideways $156.00d. (They tally both the checks and the deposit slips.) Even more fun when the person who thought they were depositing $256.00d bounces checks because they’re short $156.00d
B: Proof operator scans check written out as $3FE.0A and gets totally tripped up and blows their 15 checks per minute work rate and misses out on a promotion.
Thanks for this! It gave me a good laugh. Several actually.
If everyone looks at the number field and it doesn’t have to be right, what’s to stop someone from writing in a number larger or smaller depending on the situation…? Just so the words are right…
$F.5F!? What are you talking about? It only takes $E.F33333… for a subscription. Is the special deal still on? If so, only $7.71.
Drat, I must correct myself. The number 13.01 expressed in hexadecimal is in fact D.028F5C…
Sorry for any trouble this may have caused. (No late fees for anyone, I hope.)