[BFatts]

I think you're reading it wrong. I think the intended meaning was that it's accurate for real numbers up to, but not including, the final digit"

That's how I read it.

[emiliobumachar]

Many real numbers have an infinite number of digits

[LASR]

I think you're missing the point. Using the example above. 1/3 has no final digit. 0.333333 repeating infinitely.

So how do you then store this number to the final digit or final -1 digit using this mechanism?