# Why doesn't Float() work the same as Integer()? **URL:** \ **Category:** Ruby\ **Created:** [May 19, 2008, 10:49pm UTC](https://www.ruby-forum.com/t/why-doesnt-float-work-the-same-as-integer/138062 "2008-05-19T22:49:53Z")\ **Posts on this page:** 6\ **Page:** 2
**Author:** ![Michael\_WSRyder](https://www.ruby-forum.com/letter_avatar_proxy/v4/letter/m/53a042/32.png) [@Michael\_WSRyder](https://www.ruby-forum.com/u/Michael_WSRyder)\ **Post date:** [May 27, 2008, 8:26pm UTC](https://www.ruby-forum.com/t/why-doesnt-float-work-the-same-as-integer/138062/21 "2008-05-27T20:26:25Z")
Tim H. wrote: > Michael W. Ryder wrote: > > > I can not see how you can say that 0.1 != 1/10. I tried looking up the > > standard but the paper I looked at, about implementing the standard in a > > language, made no mention of converting floating point numbers to > > rational numbers. > > Ruby uses binary numbers, not decimal numbers. In binary, 1/10 cannot be > represented exactly, just like 1/3 cannot be represented exactly in decimal. But if I told you that 10 dimes does not equal $1 you would freak. I know that computers do not normally represent fractional numbers correctly, but part of that is the fault of the programmers and chip designers opting for “good enough”. If all arithmetic on a computer was done using something like BCD there would not be this problem. Agreed that in the deep dark past using something like BCD was noticeably slower but with the raw power available today, most of which is wasted there is no reason to accept second or third best. Anyway, there is no way for you, me, or a computer program to know if 0.1 is 1/10 or .999999999999999 or 1.00000000000001 so one can only choose one and hope that it is the right choice. Personally, as someone who works in business, I prefer the 1/10 solution as that is the way they expect it in business. They do not want to see 10 \* .1 equaling .99999999 or 1.00000001, they have to see 1. ---
**Author:** ![Michael\_WSRyder](https://www.ruby-forum.com/letter_avatar_proxy/v4/letter/m/53a042/32.png) [@Michael\_WSRyder](https://www.ruby-forum.com/u/Michael_WSRyder)\ **Post date:** [May 27, 2008, 9:17pm UTC](https://www.ruby-forum.com/t/why-doesnt-float-work-the-same-as-integer/138062/22 "2008-05-27T21:17:22Z")
On May 27, 2008, at 11:24 AM, Michael W. Ryder wrote: > If all arithmetic on a computer was done using something like BCD > there would not be this problem How would you exactly represent 1/3 in BCD? ///ark ---
**Author:** ![Michael\_WSRyder](https://www.ruby-forum.com/letter_avatar_proxy/v4/letter/m/53a042/32.png) [@Michael\_WSRyder](https://www.ruby-forum.com/u/Michael_WSRyder)\ **Post date:** [May 27, 2008, 12:57am UTC](https://www.ruby-forum.com/t/why-doesnt-float-work-the-same-as-integer/138062/23 "2008-05-27T00:57:49Z")
Michael W. Ryder wrote: > I can not see how you can say that 0.1 != 1/10. I tried looking up the > standard but the paper I looked at, about implementing the standard in a > language, made no mention of converting floating point numbers to > rational numbers. Ruby uses binary numbers, not decimal numbers. In binary, 1/10 cannot be represented exactly, just like 1/3 cannot be represented exactly in decimal. ---
**Author:** ![Michael\_WSRyder](https://www.ruby-forum.com/letter_avatar_proxy/v4/letter/m/53a042/32.png) [@Michael\_WSRyder](https://www.ruby-forum.com/u/Michael_WSRyder)\ **Post date:** [May 27, 2008, 10:55pm UTC](https://www.ruby-forum.com/t/why-doesnt-float-work-the-same-as-integer/138062/24 "2008-05-27T22:55:30Z")
On May 27, 2008, at 2:39 PM, Michael W. Ryder wrote: > I think we can agree that 1/3 \* 9 = 3 exactly, not some > approximation. we can, but it just pushes the problem back further when you re- introduce irrational numbers like pi and systems that are, by definition, approximations, like calculus. the reality is that any computation system _must_ handle approximations and handle them well. IEEE floating point numbers are a useful way to do just that for classes of problems that are larger than representing fractions. regards. a @ [http://codeforpeople.com/](http://codeforpeople.com/) ---
**Author:** ![Michael\_WSRyder](https://www.ruby-forum.com/letter_avatar_proxy/v4/letter/m/53a042/32.png) [@Michael\_WSRyder](https://www.ruby-forum.com/u/Michael_WSRyder)\ **Post date:** [May 28, 2008, 12:01am UTC](https://www.ruby-forum.com/t/why-doesnt-float-work-the-same-as-integer/138062/25 "2008-05-28T00:01:57Z")
Michael W. Ryder wrote: > > > > 0.1 is 1/10 or .999999999999999 or 1.00000000000001 so one can only > choose one and hope that it is the right choice. Personally, as someone > who works in business, I prefer the 1/10 solution as that is the way > they expect it in business. They do not want to see 10 \* .1 equaling > .99999999 or 1.00000001, they have to see 1. I found this interesting paper “Performance Characterization of Decimal Arithmetic in Commercial Java Workloads” here: [[IEEE Xplore Login](http://ieeexplore.ieee.org/Xplore/login.jsp?url=/iel5/4211006/4211007/04211022.pdf?tp=&isnumber=&arnumber=4211022)] I don’t have an account so I can’t read the paper, but I see this interesting tidbit in the summary: “In this paper, we present detailed performance characteristics and we conclude that, relative to total application performance, the overhead of using software decimal implementations is low, and at least from the point of view of these workloads, there is insufficient performance justification to pursue hardware solutions.” ---
**Author:** ![Michael\_WSRyder](https://www.ruby-forum.com/letter_avatar_proxy/v4/letter/m/53a042/32.png) [@Michael\_WSRyder](https://www.ruby-forum.com/u/Michael_WSRyder)\ **Post date:** [May 27, 2008, 10:40pm UTC](https://www.ruby-forum.com/t/why-doesnt-float-work-the-same-as-integer/138062/26 "2008-05-27T22:40:47Z")
Mark W. wrote: > On May 27, 2008, at 11:24 AM, Michael W. Ryder wrote: > > > If all arithmetic on a computer was done using something like BCD > > there would not be this problem > > How would you exactly represent 1/3 in BCD? > > ///ark The same way that the current binary system represents the number or numbers like pi, as an approximation. My point was that .1 is a real number that can be accurately represented fairly simply using something like BCD or rational numbers without having to worry about the approximations and the corrections necessary in the current representation. My module to represent rational numbers will convert decimal numbers to rationals without having to worry that it isn’t IEEE format. I am not worried that it isn’t “correct” according to Computer Science thinking as the program is for my learning. I think we can agree that 1/3 \* 9 = 3 exactly, not some approximation. [Previous page](https://www.ruby-forum.com/t/why-doesnt-float-work-the-same-as-integer/138062.md?page=1)