# [R] Floating points and floor() ?

Petr Savicky savicky at praha1.ff.cuni.cz
Fri Mar 4 09:16:12 CET 2011

```On Thu, Mar 03, 2011 at 06:23:36PM -0800, Folkes, Michael wrote:
> Perhaps somebody could clarify for me if the following is a floating
> point matter or otherwise, and how am I to correct for it?
>
> > floor(100*.1)
> [1] 10
>
> > 100*(1.0-.9)
> [1] 10
>
> > floor(100*(1-0.9))
> [1] 9

As others pointed out, 0.1 is not exactly representable in base 2,
so we get

formatC(0.1, digits=20)
[1] "0.10000000000000000555"

formatC(100*0.1, digits=20, width=-1)
[1] "10"

formatC(100*(1 - 0.9), digits=20)
[1] "9.9999999999999982236"

A correct result may be obtained, if you reorganize your
calculation, so that all intermediate results are integers
and the inaccurate division is only the last operation. Then,
floor(n/10) will be correct and also n %/% 10 may be used.

Alternatively, if you work with decimal numbers with 1 or 2
decimal digits, then also floor(round(x, 1)) or floor(round(x, 2))
work correctly, if x is not too large.

See FAQ 7.31

http://cran.r-project.org/doc/FAQ/R-FAQ.html#Why-doesn_0027t-R-think-these-numbers-are-equal_003f

and

http://rwiki.sciviews.org/doku.php?id=misc:r_accuracy:decimal_numbers

for further examples and some hints.

Hope this helps.

Petr Savicky.

```