Il existe 4 périodes de 27 chiffres pour n/109 en base 5.

Pour toutes les fractions de n/109 en base 5, la période de 1/109 revient alors 27 fois (en orange)

1/109=0,001033133242110440201300321...

2/109=0,002121322034221430403101142...

3/109=0,003210010331332421104402013...

4/109=0,004243144123443411311202334...

5/109=0,010331332421104402013003210...

6/109=0,011420021213220342214304031...

7/109=0,013003210010331332421104402...

8/109=0,014041343302442323122410223...

9/109=0,020130032100103313324211044...

10/109=0,021213220342214304031011420...

11/109=0,022301404134330244232312241...

12/109=0,023340042431441234434113112...

13/109=0,024423231224102230140413433...

14/109=0,031011420021213220342214304...

15/109=0,032100103313324211044020130...

16/109=0,033133242110440201300321001...

17/109=0,034221430403101142002121322...

18/109=0,040310114200212132203422143...

19/109=0,041343302442323122410223014...

20/109=0,042431441234434113112023340...

21/109=0,044020130032100103313324211...

22/109=0,100103313324211044020130032...

23/109=0,101142002121322034221430403...

24/109=0,102230140413433024423231224...

25/109=0,103313324211044020130032100...

26/109=0,104402013003210010331332421...

27/109=0,110440201300321001033133242...

28/109=0,112023340042431441234434113...

29/109=0,113112023340042431441234434...

30/109=0,114200212132203422143040310...

31/109=0,120233400424314412344341131...

32/109=0,121322034221430403101142002...

33/109=0,122410223014041343302442323...

34/109=0,123443411311202334004243144...

35/109=0,130032100103313324211044020...

36/109=0,131120233400424314412344341...

37/109=0,132203422143040310114200212...

38/109=0,133242110440201300321001033...

39/109=0,134330244232312241022301404...

40/109=0,140413433024423231224102230...

41/109=0,142002121322034221430403101...

42/109=0,143040310114200212132203422...

43/109=0,144123443411311202334004243...

44/109=0,200212132203422143040310114...

45/109=0,201300321001033133242110440...

46/109=0,202334004243144123443411311...

47/109=0,203422143040310114200212132...

48/109=0,210010331332421104402013003...

49/109=0,211044020130032100103313324...

50/109=0,212132203422143040310114200...

51/109=0,213220342214304031011420021...

52/109=0,214304031011420021213220342...

53/109=0,220342214304031011420021213...

54/109=0,221430403101142002121322034...

55/109=0,223014041343302442323122410...

56/109=0,224102230140413433024423231...

57/109=0,230140413433024423231224102...

58/109=0,231224102230140413433024423...

59/109=0,232312241022301404134330244...

60/109=0,233400424314412344341131120...

61/109=0,234434113112023340042431441...

62/109=0,241022301404134330244232312...

63/109=0,242110440201300321001033133...

64/109=0,243144123443411311202334004...

65/109=0,244232312241022301404134330...

66/109=0,300321001033133242110440201...

67/109=0,301404134330244232312241022...

68/109=0,302442323122410223014041343...

69/109=0,304031011420021213220342214...

70/109=0,310114200212132203422143040...

71/109=0,311202334004243144123443411...

72/109=0,312241022301404134330244232...

73/109=0,313324211044020130032100103...

74/109=0,314412344341131120233400424...

75/109=0,321001033133242110440201300...

76/109=0,322034221430403101142002121...

77/109=0,323122410223014041343302442...

78/109=0,324211044020130032100103313...

79/109=0,330244232312241022301404134...

80/109=0,331332421104402013003210010...

81/109=0,332421104402013003210010331...

82/109=0,334004243144123443411311202...

83/109=0,340042431441234434113112023...

84/109=0,341131120233400424314412344...

85/109=0,342214304031011420021213220...

86/109=0,343302442323122410223014041...

87/109=0,344341131120233400424314412...

88/109=0,400424314412344341131120233...

89/109=0,402013003210010331332421104...

90/109=0,403101142002121322034221430...

91/109=0,404134330244232312241022301...

92/109=0,410223014041343302442323122...

93/109=0,411311202334004243144123443...

94/109=0,412344341131120233400424314...

95/109=0,413433024423231224102230140...

96/109=0,420021213220342214304031011...

97/109=0,421104402013003210010331332...

98/109=0,422143040310114200212132203...

99/109=0,423231224102230140413433024...

100/109=0,424314412344341131120233400...

101/109=0,430403101142002121322034221...

102/109=0,431441234434113112023340042...

103/109=0,433024423231224102230140413...

104/109=0,434113112023340042431441234...

105/109=0,440201300321001033133242110...

106/109=0,441234434113112023340042431...

107/109=0,442323122410223014041343302...

108/109=0,443411311202334004243144123...

On remarque que le produit du nombre de périodes (4) et de leurs longueurs (27) est égal à 108 et donc au premier -1.