Table Command Not Working as Expected

Questions
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1

This may be a very basic question, but it is driving me nuts. I’ve created a minimal example that demonstrates the issue.

I’m creating a list of numbers (to use as Ticks in a plot) as follows:

Table[y, {y, -0.50, 0.50, 0.10}]

That works exactly as I would expect, passing through exactly zero, giving the output below:

In[291]:=  Table[y, {y, -0.50, 0.50, 0.10}]

Out[291]= {-0.5, -0.4, -0.3, -0.2, -0.1, 0., 0.1, 0.2, 0.3, 0.4, 0.5}

However, this does not work as expected:

 Table[y, {y, -0.60, 0.60, 0.10}]

That one does not pass through zero, and I don’t understand why. Here is the output:

In[292]:=  Table[y, {y, -0.60, 0.60, 0.10}]

Out[292]= {-0.6, -0.5, -0.4, -0.3, -0.2, -0.1, 1.11022*10^-16, 0.1, 0.2, 0.3, 0.4, 0.5, 0.6}

I know that I can fix that by using Round[] as follows:

Table[N[Round[y, 10^-4]], {y, -0.60, 0.60, 0.10}]

and here is the output (note that it seems that N[] is required to avoid fractions):

In[295]:=  Table[N[Round[y, 10^-4]], {y, -0.60, 0.60, 0.10}]

Out[295]= {-0.6, -0.5, -0.4, -0.3, -0.2, -0.1, 0., 0.1, 0.2, 0.3, 0.4, 0.5, 0.6}

So, my question is why, when you go from -0.5 to 0.5 in steps of 0.10 does it pass through 0, but when you go from -0.6 to 0.6 in steps of 0.10 it does not? Seems to me that I should get the output shown in the last box without having to use Round[].

2

Remember that with a command like

Table[y, {y, -0.50, 0.50, 0.10}]

or in fact any command that is using floating point numbers, the numbers that are actually being used internally are the floating point representaiton of those numbers: not necessarilly what you see on the screen. Thus you have the following going on internally in the computation for the 0.6 and the 0.5 case respectively:

In[1]:= InputForm[6*0.1]
Out[1]//InputForm=
0.6000000000000001


In[2]:= InputForm[5*0.1]


Out[2]//InputForm=
0.5
3

Exactly -- I agree with David. I suspect the 0.5 case generated a “more exact” result because it is a power of 2.

In[5]:= Table[y, {y, -0.60, 0.60, 0.10}]

Out[5]= {-0.6, -0.5, -0.4, -0.3, -0.2, -0.1, 
 1.11022*10^-16, 0.1, 0.2, 0.3, 0.4, 0.5, 0.6}

In[6]:= % // Chop

Out[6]= {-0.6, -0.5, -0.4, -0.3, -0.2, -0.1, 0, 0.1, 0.2, 0.3, 0.4, \
0.5, 0.6}

In[7]:= Table[y, {y, -6/10, 6/10, 1/10}]

Out[7]= {-(3/5), -(1/2), -(2/5), -(3/10), -(1/5), -(1/
  10), 0, 1/10, 1/5, 3/10, 2/5, 1/2, 3/5}

In[8]:= % // N

Out[8]= {-0.6, -0.5, -0.4, -0.3, -0.2, -0.1, 0., 0.1, 0.2, 0.3, 0.4, \
0.5, 0.6}
4

Thanks guys, that makes perfect sense even though it never would have occurred to me.