[R] why the base::round(0.015, 2) returns 0.02?

[Duncan Murdoch]

On 28/11/2018 8:49 AM, Philipp Upravitelev wrote:
> Dear colleagues,
> could you help me with the function base::round()? I can't understand how
> it works.
> 
> For example, when I want to round 0.015 to the second digit, base::round()
> returns 0.02.
> 
> But the real representation of the 0.015 is different:
>> sprintf('%.20f', 0.015)
> [1] "0.01499999999999999944"
>> 0.015 == 0.01499999999999999944
> [1] TRUE
>> round(0.015, 2)
> [1] 0.02

This calculation is informative:

100*0.015 - 1.5

which gives 0 on my system.  So even though 0.015 isn't exactly 
representable, when you multiply by 100, you get the exactly correct 
result.  Then the apparent rule for round(x, 2) is:  multiply by 100, 
round to an integer, divide by 100.

Duncan Murdoch

> 
> Therefore, according to the arithmetic rules, rounded 0.014 to the second
> digit is 0.01. Also, the round() function in other programming languages
> (Python, Java) returns 0.01. It is a bit counterintuitive but
> mathematically correct.
> 
> I'll be very pleased if you could help me to figure out why the
> base::round(0.015, 2) returns 0.02 and what is the purpose of this feature.
> 
> Best regards,
> Philipp Upravitelev
> 
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> 
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