Something that I am sure is obvious to jonathang, but may not have occurred to others, is that the first two numbers of the reciprocal always add up to the same, or in a couple of cases something memorably obvious:
01 19
02 20
03 21
04 22
05 23
06 24
07 25
08 26
09 27
10 28
11 29
12 30
13 31
14 32
15 33
16 34
17 35
This means that the easiest way of doing the calculation is to learn the above list (with the prompt/reality check that the numbers add up) then add (always add!) the third digit.
Oh, and jonathang, I'll accept your wrist slap for not answering the question as read, OK?