Hi The problem is that people using Excel or probably other such spreadsheets do not encounter this behaviour as Excel silently rounds all your calculations and makes approximate comparison without telling it does so. Therefore most people usually do not have any knowledge of floating point numbers representation.
Cheers Petr -----Original Message----- From: R-help [mailto:r-help-boun...@r-project.org] On Behalf Of Paul Johnson Sent: Thursday, April 20, 2017 11:56 PM To: R-help <r-help@r-project.org> 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. 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