# Floor function not returning correct value

Something very strange is happening as I evaluate the Floor function:

(9.2 - 8)/1.2
Floor[(9.2 - 8)/1.2]


returns:

1.

0


so I did the following:

Floor[1]
Floor[1.0]
Floor[1.2/1.2]


returning

1

1

1


Does anybody know what is happening? Am I doing something wrong here? I also tried the following and got the same confusing result:

x = (9.2 - 8)/1.2
Floor[x]

1.

0


and

In[57]:= Floor[(10.2 - 9.0)/1.2]

Out[57]= 0


but

In[59]:= Floor[(10.4 - 9.0)/1.4]

Out[59]= 1


I'm getting so confused that sometimes I doubt myself when doing this simple operations in my head... Any information about this will be highly appreciated.

• Examine the output of (9.2 - 8)/1.2 // FullForm. – Carl Woll Mar 11 at 21:48
• You might find (9.2 - 8)/1.2 // FullForm illuminating—Mathematica does this occasionally annoying thing where it rounds numerical output in output cells by default. As to why (9.2 - 8)/1.2 is less than one, I'm not totally sure beyond "implementation details", and that's still worth getting an explanation for. EDIT: I see @CarlWoll beat me to it by 15 seconds... :) – thorimur Mar 11 at 21:49
• Oh, so it's related to the order of evaluation... Thank you very very much @CarlWoll and @thorimur, I think Round[x,0.1] will do the trick for me :D – Sofi Ixchel Mar 11 at 21:58
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As it was suggested by @CarlWoll and @thorimur in the comments, I evaluated:

(9.2 - 8)/1.2 // FullForm


which returns:

0.9999999999999994


I'm not really sure why, but I suspect that this is related to the order in which Mathematica evaluates each operation. Since 9.2/1.2 and 8/1.2 have no finite decimal expansion, apparently Mathematica truncates this expressions and rounds them when showing the final answer. So I decided to round them myself before plugging them in the Floor function as follows:

Floor[Round[(9.2 - 8)/1.2, 0.1]]


resulting in:

1


I still have no clue why Mathematica would distribute the 1/1.2 into the subtraction apparently ignoring the parenthesis, but I suppose it's usually better when working with large numbers...

• It's not that it's distributing the 1.2, it's that 9.2 - 8 is slightly less than 1.2 when using machine precision numbers. Try just 9.2 - 8//FullForm and you'll get 1.1999999999999993. If you use Round (as you already did) or Rationalize to get exact numbers, or enter exact numbers yourself (Floor[(92 - 80)/12]`), Mathematica will be able to return the correct value. – MassDefect Mar 12 at 4:51