Question about floating point

[MRAB]

On 2018-08-28 15:11, Frank Millman wrote:
> Hi all
> 
> I know about this gotcha -
> 
>>>> x = 1.1 + 2.2
>>>> x
> 3.3000000000000003
> 
> According to the docs, the reason is that "numbers like 1.1 and 2.2 do not
> have exact representations in binary floating point."
> 
> So when I do this -
> 
>>>> y = 3.3
>>>> y
> 3.3
> 
> what exactly is happening? What is 'y' at this point?
> 
> Or if I do this -
> 
>>>> z = (1.1 + 2.2) * 10 / 10
>>>> z
> 3.3
> 
> What makes it different from the first example?
> 
There's a bit of rounding going on in the last few digits. For example:

 >>> 1.1
1.1
 >>> _ - 1
0.10000000000000009
 >>> 0.1
0.1
 >>> _ * 10 - 1
0.0