n       1/n = decimal
1 1/1 = .9
2 1/2 = .5
3 1/3 = .3 2/3 =.6
4 1/4 = .25 3/4 =.75
5 1/5 = .2 2/5 =.4 3/5 =.6   4/5 =.8
6 1/6 = .16 5/6 =.83
7 1/7 = .142857 2/7 =.285714   3/7 =.428571   4/7 =.571428   5/7 =.714285   6/7 =.857142
8 1/8 = .125
9 1/9 = .1 2/9 =.2 4/9 =.4   5/9 =.5   7/9 =.7   8/9 =.8
10 1/10 = .1
11 1/11 = .09 2/11 =.18   3/11 =.27   4/11 =.36   5/11 =.45   6/11 =.54   7/11 =.63   8/11 =.72   9/11 =.81   10/11 =.90
12 1/12 = .083
13 1/13 = .076923
14 1/14 = .0714285
15 1/15 = .06
16 1/16 = .0625
17 1/17 = .0588235294117647
18 1/18 = .05
19 1/19 = .052631578947368421
20 1/20 = .05

Multiples of a fraction that are not simplifiable have the same recurrence lengths.
e.g. 1/7, 2/7, 3/7, 4/7, 5/7, 6/7
e.g. 1/6, 5/6
e.g.

e.g. difference between 1/8 and 1/9 is 1/72

Repeating decimals:
.d1 = d1 / 9      E.g. .77777...=.7 = 7/9
.d1d2 = d1d2 / 99      E.g. .858585...=.85 = 85/99
.d1d2d3 = d1d2d3 / 999      E.g. .492492492...=.492 = 492/999

Convert decimal whose repeating recurrence doesn't start immediately after decimal point: 

x = .xyzddddd...      ddddd is the recurrence of length n. m is length of non-recurrence start
     m   n
10^m+n x = xyzddddd.ddddd...
- 10^m x =      xyz.ddddd...
------------------------------
                  F.0
x = F / 10^m+n-10^m

Ex.  x = .1234987987987...   
          m=4  n=3
 10^7 x = 1234987.987987...
-10^4 x =    1234.987987...
----------------------------
          1233753
10^7-10^4=10000000-10000=9990000
x = 1233753 / 9990000