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