floating point - Why does python show 0.2 + 0.2 as 0.4? -


i think understood why 0.1 + 0.2 0.30000000000000004, following same logic why 0.2 + 0.2 = 0.4? isn't 0.2 value can't in binary base? thank time.

to 0.2 need sum binary fractions of 2. here first few:

decimal   binary 1       = 1 0.5     = 0.1 0.25    = 0.01 0.125   = 0.001 0.0625  = 0.0001

so, 0.2, need sum

0.125 + 0.0625 = 0.187500

the next binary fraction 0.03125. if sum that, it's large (> 0.2), next 1 0.015625. following one, 0.0078125 ok, so

0.125 + 0.0625 + 0.0078125 = 0.195312

and on. have skipped 0.5 (gives 0), , 0.25 (another 0), did use 0.125 (1) , 0.0625 (1). again, skipped 2 values (00) , used next 1 (1)...

but, whatever do, cannot represent 0.2 exact binary numner. have continue , continue... if don't continue infinitely, representation not 0.2...

now try 0.25 or 0.25...

now why seeing different things in modern pythons (>= 2.7, , >= 3), comes internal change:

in versions prior python 2.7 , python 3.1, python rounded value 17 significant digits, giving ‘0.10000000000000001’. in current versions, python displays value based on shortest decimal fraction rounds correctly true binary value, resulting in ‘0.1’.

see this article, bottom of page.


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