Il existe 9 périodes de 12 chiffres pour n/109 en base 8.

Pour toutes les fractions de n/109 en base 8, la période de 1/109 revient alors 12 fois (en orange)

1/109=0,004544773233...

2/109=0,011311766466...

3/109=0,016056761721...

4/109=0,022623755154...

5/109=0,027370750407...

6/109=0,034135743642...

7/109=0,040702737075...

8/109=0,045447732330...

9/109=0,052214725563...

10/109=0,056761721016...

11/109=0,063526714251...

12/109=0,070273707504...

13/109=0,075040702737...

14/109=0,101605676172...

15/109=0,106352671425...

16/109=0,113117664660...

17/109=0,117664660113...

18/109=0,124431653346...

19/109=0,131176646601...

20/109=0,135743642034...

21/109=0,142510635267...

22/109=0,147255630522...

23/109=0,154022623755...

24/109=0,160567617210...

25/109=0,165334612443...

26/109=0,172101605676...

27/109=0,176646601131...

28/109=0,203413574364...

29/109=0,210160567617...

30/109=0,214725563052...

31/109=0,221472556305...

32/109=0,226237551540...

33/109=0,233004544773...

34/109=0,237551540226...

35/109=0,244316533461...

36/109=0,251063526714...

37/109=0,255630522147...

38/109=0,262375515402...

39/109=0,267142510635...

40/109=0,273707504070...

41/109=0,300454477323...

42/109=0,305221472556...

43/109=0,311766466011...

44/109=0,316533461244...

45/109=0,323300454477...

46/109=0,330045447732...

47/109=0,334612443165...

48/109=0,341357436420...

49/109=0,346124431653...

50/109=0,352671425106...

51/109=0,357436420341...

52/109=0,364203413574...

53/109=0,370750407027...

54/109=0,375515402262...

55/109=0,402262375515...

56/109=0,407027370750...

57/109=0,413574364203...

58/109=0,420341357436...

59/109=0,425106352671...

60/109=0,431653346124...

61/109=0,436420341357...

62/109=0,443165334612...

63/109=0,447732330045...

64/109=0,454477323300...

65/109=0,461244316533...

66/109=0,466011311766...

67/109=0,472556305221...

68/109=0,477323300454...

69/109=0,504070273707...

70/109=0,510635267142...

71/109=0,515402262375...

72/109=0,522147255630...

73/109=0,526714251063...

74/109=0,533461244316...

75/109=0,540226237551...

76/109=0,544773233004...

77/109=0,551540226237...

78/109=0,556305221472...

79/109=0,563052214725...

80/109=0,567617210160...

81/109=0,574364203413...

82/109=0,601131176646...

83/109=0,605676172101...

84/109=0,612443165334...

85/109=0,617210160567...

86/109=0,623755154022...

87/109=0,630522147255...

88/109=0,635267142510...

89/109=0,642034135743...

90/109=0,646601131176...

91/109=0,653346124431...

92/109=0,660113117664...

93/109=0,664660113117...

94/109=0,671425106352...

95/109=0,676172101605...

96/109=0,702737075040...

97/109=0,707504070273...

98/109=0,714251063526...

99/109=0,721016056761...

100/109=0,725563052214...

101/109=0,732330045447...

102/109=0,737075040702...

103/109=0,743642034135...

104/109=0,750407027370...

105/109=0,755154022623...

106/109=0,761721016056...

107/109=0,766466011311...

108/109=0,773233004544...

On remarque que le produit du nombre de périodes (9) et de leurs longueurs (12) est égal à 108 et donc au premier -1.