Most people don't realize that the IEEE-754 single precision floating point represent real numbers with 9 decimal digits (or 23 binary digits). The double, on the other hand, represents the real numbers with 17 decimal digits.
This means that the double error UPPER BOUND is (0.00000000000000001)/2 per operation. But in reality the error is lower because of the rounding operations.
Also, it is posssible to extend the range using denormals, but most (all?) compilers disable them when compiling with anything other than O0 to avoid performance degradation.
The overheads associate with dealing with non-float types for most applications might not be worth it the cost and risk. If course, if the language are working with provides a currency type, go for it. But if doesn't , there is no need to worry.
No, they don't. They merely can be converted back to decimal with those numbers of significant digits without loss of information.
That is important because (a) if this matters, you have to make sure you actually control the number of significant digits when converting to decimal, or you might end up with a different decimal, and (b) the operations that you do on the floats do not reliably behave as if there was the supposedly represented decimal number stored in them.
Now, sure, you can use floats for currency, if you know what you are doing, but the point of the warning against it is that you have to know what you are doing, and chances are you don't, or if you do, then you know where you can ignore it anyway.
(That is, unless you mean nothing more than that you can encode the information contained in an n-digit decimal in a float/double--which of course is true, but not particular to floating point numbers, as any state with a certain number of bits can, of course, encode any information of no more than that many bits, somehow.)
Floating Points are hard. There is a study done with academics that shows that even researches that works with float point everyday forget about the format intricacies. And the study didn't even look into the compiler mess.
But I agree with you, some (a lot?) of caution is needed when working with float point is good.
$ ruby -e 'pp 87e12 + 0.01'
I really see no reason to use any other representation for currency than decimal fixed point. Store the amount as mils or whatever unit suits your use case.
For the vast majority of person, there is no need to worry so much about using fp to represent currencies. There are other issues with float that will bite you in your back before precision became one of them.
The problem is that rounding is kind of a big deal in certain financial contexts, and the process of rounding can greatly magnify floating point's decimal precision problems when you're dealing with numbers that are close to the .5's.
When I said up above that there are some contexts where IEEE floats are fine, those contexts are largely ones where you never have to round, or where you can guarantee that an accountant is never going to see or care how you rounded. So, to an approximation: Go ahead and fearlessly implement the Black-Scholes formula using doubles, but never, ever use them to do something simple like calculating an invoice.
I worked with a CSV containing, among other things, phone numbers. A coworker called and complained that the phone numbers were all wrong. He'd edited the thing in MS Excel, which promptly converted the phone numbers to floating point with a loss in precision. When he saved it, those new numbers were happily written back to the disk.