Trouble with numeric for loop and step variant?

I've been messing around with numeric for loops (including the use of the step variant), and came across what I thought to be a rather strange result...

For example, if I say something like:

-- From 0-1, increasing i by 0.1 every iteration (i like the look of fractions better than decimal points)

for i = 0,1,1/10 do
    print(i)
end

As expected, the code above prints the following:

0, 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, 1

However, when working with larger decimal places (i.e, 0.01 and smaller), the loop will end on i - x/step. For example:

-- This time dividing the step into hundreths...

for i = 0,1,1/100 do
    print(i)
end

Except this time instead of i starting at 0 and ending on 1, it will start at 0 and end on 0.99. Is there any specific reason for this? And like I said, same goes for all other larger decimal places:

for i = 0,1,1/1000 do print(i) end

0, 0.001, 0.002 ... 0.999

Question

How can I be 100% certain that my for loop will iterate having it's control variable equal my start value, all the way through my end value while using the step variant? (i.e, 0, 1, 1/100 looping 0 - 1 in hundredths) If anyone has some insight on this, I'd really appreciate it.