# [R] Interesting quirk with fractions and rounding

Hervé Pagès hpages at fredhutch.org
Fri Apr 21 05:08:29 CEST 2017

```Also note that we see the same thing in Ruby:

irb(main):001:0> 100*(23/40)
=> 0
irb(main):002:0> 100.0*(23.0/40.0)
=> 57.49999999999999
irb(main):003:0> (100.0*23.0)/40.0
=> 57.5

and in C:

hpages at latitude:~\$ cat test.c
#include <stdio.h>
main() {
printf("%.15f\n", 100.0 * (23.0 / 40.0));
printf("%.15f\n", (100.0 * 23.0) / 40.0);
}

hpages at latitude:~\$ gcc test.c

hpages at latitude:~\$ ./a.out
57.499999999999993
57.500000000000000

These rounding errors are intrinsically related to how computers
do floating point arithmetic.

H.

On 04/20/2017 03:34 PM, Michael Hannon wrote:
> I might add that things that *look* like integers in R are not really
> integers, unless you explicitly label them as such:
>
>> str(20)
>  num 20
>
>> str(20.5)
>  num 20.5
>
>> str(20L)
>  int 20
>>
>
> I think that Python 2 will do integer arithmetic on things that look
> like integers:
>
> \$ python2
> .
> .
> .
>>>> 30 / 20
> 1
>>>>
>
> But that behavior has changed in Python 3:
>
> \$ python3
> .
> .
> .
>>>> 30 / 20
> 1.5
>>>>
>
> -- Mike
>
>
> On Thu, Apr 20, 2017 at 3:20 PM, Nordlund, Dan (DSHS/RDA)
> <NordlDJ at dshs.wa.gov> wrote:
>> This is FAQ 7.31.  It is not a bug, it is the unavoidable problem of accurately representing floating point numbers with a finite number of bits of precision.  Look at the following:
>>
>>> a <- 100*(23/40)
>>> b <- (100*23)/40
>>> print(a,digits=20)
>> [1] 57.499999999999993
>>> print(b,digits=20)
>> [1] 57.5
>>>
>>
>> Your example with all.equal evaluates TRUE because all.equal uses a 'fuzz factor'.  From the all.equal man page
>>
>> "all.equal(x, y) is a utility to compare R objects x and y testing 'near equality'."
>>
>>
>>
>> Dan
>>
>> Daniel Nordlund, PhD
>> Research and Data Analysis Division
>> Services & Enterprise Support Administration
>> Washington State Department of Social and Health Services
>>
>>
>>> -----Original Message-----
>>> From: R-help [mailto:r-help-bounces at r-project.org] On Behalf Of Paul
>>> Johnson
>>> Sent: Thursday, April 20, 2017 2:56 PM
>>> To: R-help
>>> Subject: [R] Interesting quirk with fractions and rounding
>>>
>>> Hello, R friends
>>>
>>> My student unearthed this quirk that might interest you.
>>>
>>> I wondered if this might be a bug in the R interpreter. If not a bug,
>>> it certainly stands as a good example of the dangers of floating point
>>> numbers in computing.
>>>
>>> What do you think?
>>>
>>>> 100*(23/40)
>>> [1] 57.5
>>>> (100*23)/40
>>> [1] 57.5
>>>> round(100*(23/40))
>>> [1] 57
>>>> round((100*23)/40)
>>> [1] 58
>>>
>>> The result in the 2 rounds should be the same, I think.  Clearly some
>>> digital number devil is at work. I *guess* that when you put in whole
>>> numbers and group them like this (100*23), the interpreter does
>>> integer math, but if you group (23/40), you force a fractional
>>> division and a floating point number. The results from the first 2
>>> calculations are not actually 57.5, they just appear that way.
>>>
>>> Before you close the books, look at this:
>>>
>>>> aa <- 100*(23/40)
>>>> bb <- (100*23)/40
>>>> all.equal(aa,bb)
>>> [1] TRUE
>>>> round(aa)
>>> [1] 57
>>>> round(bb)
>>> [1] 58
>>>
>>> I'm putting this one in my collection of "difficult to understand"
>>> numerical calculations.
>>>
>>> If you have seen this before, I'm sorry to waste your time.
>>>
>>> pj
>>> --
>>> Paul E. Johnson   https://urldefense.proofpoint.com/v2/url?u=http-3A__pj.freefaculty.org&d=DwICAg&c=eRAMFD45gAfqt84VtBcfhQ&r=BK7q3XeAvimeWdGbWY_wJYbW0WYiZvSXAJJKaaPhzWA&m=h2uDuHofumYjJ48NvOaART10-esHowpTtp37cGtD3yQ&s=mCvk8xBulYqnlArSRFzabdeCvvmH9UFJ0kxrxsNC0SE&e=
>>> Director, Center for Research Methods and Data Analysis
>>> https://urldefense.proofpoint.com/v2/url?u=http-3A__crmda.ku.edu&d=DwICAg&c=eRAMFD45gAfqt84VtBcfhQ&r=BK7q3XeAvimeWdGbWY_wJYbW0WYiZvSXAJJKaaPhzWA&m=h2uDuHofumYjJ48NvOaART10-esHowpTtp37cGtD3yQ&s=rtQq4X4vty_dsRAWEsD_-ZZh7UDdnlLKyBllAl3i5eY&e=
>>>
>>> To write to me directly, please address me at pauljohn at ku.edu.
>>>
>>> ______________________________________________
>>> R-help at r-project.org mailing list -- To UNSUBSCRIBE and more, see
>>> https://urldefense.proofpoint.com/v2/url?u=https-3A__stat.ethz.ch_mailman_listinfo_r-2Dhelp&d=DwICAg&c=eRAMFD45gAfqt84VtBcfhQ&r=BK7q3XeAvimeWdGbWY_wJYbW0WYiZvSXAJJKaaPhzWA&m=h2uDuHofumYjJ48NvOaART10-esHowpTtp37cGtD3yQ&s=efyHNH41uiy_mo_2RYV1aQU3sMi2yKoAfK7LMdoK5eM&e=
>>> guide.html
>>> and provide commented, minimal, self-contained, reproducible code.
>>
>> ______________________________________________
>> R-help at r-project.org mailing list -- To UNSUBSCRIBE and more, see
>> https://urldefense.proofpoint.com/v2/url?u=https-3A__stat.ethz.ch_mailman_listinfo_r-2Dhelp&d=DwICAg&c=eRAMFD45gAfqt84VtBcfhQ&r=BK7q3XeAvimeWdGbWY_wJYbW0WYiZvSXAJJKaaPhzWA&m=h2uDuHofumYjJ48NvOaART10-esHowpTtp37cGtD3yQ&s=efyHNH41uiy_mo_2RYV1aQU3sMi2yKoAfK7LMdoK5eM&e=
>> and provide commented, minimal, self-contained, reproducible code.
>
> ______________________________________________
> R-help at r-project.org mailing list -- To UNSUBSCRIBE and more, see
> https://urldefense.proofpoint.com/v2/url?u=https-3A__stat.ethz.ch_mailman_listinfo_r-2Dhelp&d=DwICAg&c=eRAMFD45gAfqt84VtBcfhQ&r=BK7q3XeAvimeWdGbWY_wJYbW0WYiZvSXAJJKaaPhzWA&m=h2uDuHofumYjJ48NvOaART10-esHowpTtp37cGtD3yQ&s=efyHNH41uiy_mo_2RYV1aQU3sMi2yKoAfK7LMdoK5eM&e=
> and provide commented, minimal, self-contained, reproducible code.
>

--
Hervé Pagès

Program in Computational Biology
Division of Public Health Sciences
Fred Hutchinson Cancer Research Center
1100 Fairview Ave. N, M1-B514
P.O. Box 19024
Seattle, WA 98109-1024

E-mail: hpages at fredhutch.org
Phone:  (206) 667-5791
Fax:    (206) 667-1319

```