Re: 0.99999999/1.0001 - 0.99999991/1.0003 =

Here is my alternative solution for this problem (not for all problems):

\frac{A}{B} - \frac{C}{D}= \frac{(AD-BC)}{BD}.

So \frac{0.99999999}{1.0001} - \frac{0.99999991}{1.0003}= \frac{(0.99999999*1.0003-0.99999991*1.0001)}{(1.0001*1.0003)}.

For this case, the ultimate digit of 0.99999999*1.0003-0.99999991*1.0001 is 6
In the denominator, the ultimate digit of 1.0001*1.0003 is 3
Therefore, the ultimate digit of the final result is 2. So it should be 2 * 0.00...01 --> Only D has the last digit of 2.

Alternatively, we can calculate each fraction, \frac{0.99999999}{1.0001} has last digit of 9, and \frac{0.99999991}{1.0003} has last digit of 7, so the final last digit is 2 --> D

This is a special problem. For example \frac{...6}{4} can have a result of ...4 or ...9. Therefore, in this case we have to calculate as aforementioned Bunuel's calculation.

In general, we can only apply this strategy only if the last digit of divisor is 1, 2 or 3.