Look at what they need to mimic a fraction inaccurately.
The fundamental mathematical nature of how binary floating point values are stored means that extremely straightforward and rational (in the mathematical sense of the term) base-10 arithmetic can surprisingly often yield results that are irrational (again, mathematically) in binary - hence why you’ll sometimes see a result of 3.000000000101325 or something like that in places where you’d expect the result to be simply 3.0
Irrational specifically means infinite non-repeating decimal values, or equivalently that a number can’t be represented as any fraction. This is independent of number system.
Sometimes “more irrational” is used as a way of saying further from those small-integer fractions by some measure, but that doesn’t really work here.
There is also Decimal floating-point arithmetic which has a larger range and better memory safety. Java, C#, Python, Ruby, etc. have built in support for it via Decimal.
Banks and big companies have to worry about round-off and fractions of a penny, so Decimal is a better solution for them. But the great unwashed like you and me will never have to worry about that, so either works.
As other people mentioned, things like the decimal structure works well, but you can also just use an int to store how many pennies something costs and convert it to dollars for display.
The same IEEE spec that introduced base-2 floating point models was updated in 2008 to include some base-10 models that eliminate these issues. Many languages already support them natively, as well as most database engines. Otherwise, you can probably find third-party-library support.
If you don’t have access to an IEEE decimal implementation, or if you just wanna be a rulebreaker, the common strategy is to just store only plain integers, and the precision level you want. So, say, if you’re just dealing with simple american dollars, you’d just make sure to always interpret the integer value as “cents”. If you need more precision than that, you might do “millicents”.
The fundamental mathematical nature of how binary floating point values are stored means that extremely straightforward and rational (in the mathematical sense of the term) base-10 arithmetic can surprisingly often yield results that are irrational (again, mathematically) in binary - hence why you’ll sometimes see a result of 3.000000000101325 or something like that in places where you’d expect the result to be simply 3.0
It’d be more correct to say round or unround.
Irrational specifically means infinite non-repeating decimal values, or equivalently that a number can’t be represented as any fraction. This is independent of number system.
Sometimes “more irrational” is used as a way of saying further from those small-integer fractions by some measure, but that doesn’t really work here.
Yep. Open your browser’s console and do
.1 + .2and you get0.30000000000000004.One of the reasons not to use floating point when working with money.
What’s the right way to do money math without floats?
Fixed-point arithmetics
There is also Decimal floating-point arithmetic which has a larger range and better memory safety. Java, C#, Python, Ruby, etc. have built in support for it via Decimal.
Banks and big companies have to worry about round-off and fractions of a penny, so Decimal is a better solution for them. But the great unwashed like you and me will never have to worry about that, so either works.
Also known as “if you ain’t storing cents, you ain’t making sense.”
As other people mentioned, things like the decimal structure works well, but you can also just use an int to store how many pennies something costs and convert it to dollars for display.
The same IEEE spec that introduced base-2 floating point models was updated in 2008 to include some base-10 models that eliminate these issues. Many languages already support them natively, as well as most database engines. Otherwise, you can probably find third-party-library support.
If you don’t have access to an IEEE decimal implementation, or if you just wanna be a rulebreaker, the common strategy is to just store only plain integers, and the precision level you want. So, say, if you’re just dealing with simple american dollars, you’d just make sure to always interpret the integer value as “cents”. If you need more precision than that, you might do “millicents”.
Use a dedicated data type or library. Some languages also have something like python’s Decimal type
>>> .1 + .2 0.30000000000000004 >>> Decimal(".1") + Decimal(".2") Decimal('0.3')i see what you’re trying to say, but that’s not what rational and irrational means (mathematically).
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Look what they need to mimic a fraction of a fraction.