Il existe 2 périodes de 53 chiffres pour n/107 en base 9.

Pour toutes les fractions de n/107 en base 9, la période de 1/107 revient alors 53 fois (en orange)

1/107=0,00672765720828441075115340302238518362687433246347131...

2/107=0,01455642541757882161231680604478137735485866503705262...

3/107=0,02238518362687433246347131006727657208284410751153403...

4/107=0,03022385183626874332463471310067276572082844107511534...

5/107=0,03705262014556425417578821612316806044781377354858665...

6/107=0,04478137735485866503705262014556425417578821612316806...

7/107=0,05262014556425417578821612316806044781377354858665037...

8/107=0,06044781377354858665037052620145564254175788216123168...

9/107=0,06727657208284410751153403022385183626874332463471310...

10/107=0,07511534030223851836268743324634713100672765720828441...

11/107=0,08284410751153403022385183626874332463471310067276572...

12/107=0,10067276572082844107511534030223851836268743324634713...

13/107=0,10751153403022385183626874332463471310067276572082844...

14/107=0,11534030223851836268743324634713100672765720828441075...

15/107=0,12316806044781377354858665037052620145564254175788216...

16/107=0,13100672765720828441075115340302238518362687433246347...

17/107=0,13773548586650370526201455642541757882161231680604478...

18/107=0,14556425417578821612316806044781377354858665037052620...

19/107=0,15340302238518362687433246347131006727657208284410751...

20/107=0,16123168060447813773548586650370526201455642541757882...

21/107=0,16806044781377354858665037052620145564254175788216123...

22/107=0,17578821612316806044781377354858665037052620145564254...

23/107=0,18362687433246347131006727657208284410751153403022385...

24/107=0,20145564254175788216123168060447813773548586650370526...

25/107=0,20828441075115340302238518362687433246347131006727657...

26/107=0,21612316806044781377354858665037052620145564254175788...

27/107=0,22385183626874332463471310067276572082844107511534030...

28/107=0,23168060447813773548586650370526201455642541757882161...

29/107=0,23851836268743324634713100672765720828441075115340302...

30/107=0,24634713100672765720828441075115340302238518362687433...

31/107=0,25417578821612316806044781377354858665037052620145564...

32/107=0,26201455642541757882161231680604478137735485866503705...

33/107=0,26874332463471310067276572082844107511534030223851836...

34/107=0,27657208284410751153403022385183626874332463471310067...

35/107=0,28441075115340302238518362687433246347131006727657208...

36/107=0,30223851836268743324634713100672765720828441075115340...

37/107=0,31006727657208284410751153403022385183626874332463471...

38/107=0,31680604478137735485866503705262014556425417578821612...

39/107=0,32463471310067276572082844107511534030223851836268743...

40/107=0,33246347131006727657208284410751153403022385183626874...

41/107=0,34030223851836268743324634713100672765720828441075115...

42/107=0,34713100672765720828441075115340302238518362687433246...

43/107=0,35485866503705262014556425417578821612316806044781377...

44/107=0,36268743324634713100672765720828441075115340302238518...

45/107=0,37052620145564254175788216123168060447813773548586650...

46/107=0,37735485866503705262014556425417578821612316806044781...

47/107=0,38518362687433246347131006727657208284410751153403022...

48/107=0,40302238518362687433246347131006727657208284410751153...

49/107=0,41075115340302238518362687433246347131006727657208284...

50/107=0,41757882161231680604478137735485866503705262014556425...

51/107=0,42541757882161231680604478137735485866503705262014556...

52/107=0,43324634713100672765720828441075115340302238518362687...

53/107=0,44107511534030223851836268743324634713100672765720828...

54/107=0,44781377354858665037052620145564254175788216123168060...

55/107=0,45564254175788216123168060447813773548586650370526201...

56/107=0,46347131006727657208284410751153403022385183626874332...

57/107=0,47131006727657208284410751153403022385183626874332463...

58/107=0,47813773548586650370526201455642541757882161231680604...

59/107=0,48586650370526201455642541757882161231680604478137735...

60/107=0,50370526201455642541757882161231680604478137735485866...

61/107=0,51153403022385183626874332463471310067276572082844107...

62/107=0,51836268743324634713100672765720828441075115340302238...

63/107=0,52620145564254175788216123168060447813773548586650370...

64/107=0,53403022385183626874332463471310067276572082844107511...

65/107=0,54175788216123168060447813773548586650370526201455642...

66/107=0,54858665037052620145564254175788216123168060447813773...

67/107=0,55642541757882161231680604478137735485866503705262014...

68/107=0,56425417578821612316806044781377354858665037052620145...

69/107=0,57208284410751153403022385183626874332463471310067276...

70/107=0,57882161231680604478137735485866503705262014556425417...

71/107=0,58665037052620145564254175788216123168060447813773548...

72/107=0,60447813773548586650370526201455642541757882161231680...

73/107=0,61231680604478137735485866503705262014556425417578821...

74/107=0,62014556425417578821612316806044781377354858665037052...

75/107=0,62687433246347131006727657208284410751153403022385183...

76/107=0,63471310067276572082844107511534030223851836268743324...

77/107=0,64254175788216123168060447813773548586650370526201455...

78/107=0,65037052620145564254175788216123168060447813773548586...

79/107=0,65720828441075115340302238518362687433246347131006727...

80/107=0,66503705262014556425417578821612316806044781377354858...

81/107=0,67276572082844107511534030223851836268743324634713100...

82/107=0,68060447813773548586650370526201455642541757882161231...

83/107=0,68743324634713100672765720828441075115340302238518362...

84/107=0,70526201455642541757882161231680604478137735485866503...

85/107=0,71310067276572082844107511534030223851836268743324634...

86/107=0,72082844107511534030223851836268743324634713100672765...

87/107=0,72765720828441075115340302238518362687433246347131006...

88/107=0,73548586650370526201455642541757882161231680604478137...

89/107=0,74332463471310067276572082844107511534030223851836268...

90/107=0,75115340302238518362687433246347131006727657208284410...

91/107=0,75788216123168060447813773548586650370526201455642541...

92/107=0,76572082844107511534030223851836268743324634713100672...

93/107=0,77354858665037052620145564254175788216123168060447813...

94/107=0,78137735485866503705262014556425417578821612316806044...

95/107=0,78821612316806044781377354858665037052620145564254175...

96/107=0,80604478137735485866503705262014556425417578821612316...

97/107=0,81377354858665037052620145564254175788216123168060447...

98/107=0,82161231680604478137735485866503705262014556425417578...

99/107=0,82844107511534030223851836268743324634713100672765720...

100/107=0,83626874332463471310067276572082844107511534030223851...

101/107=0,84410751153403022385183626874332463471310067276572082...

102/107=0,85183626874332463471310067276572082844107511534030223...

103/107=0,85866503705262014556425417578821612316806044781377354...

104/107=0,86650370526201455642541757882161231680604478137735485...

105/107=0,87433246347131006727657208284410751153403022385183626...

106/107=0,88216123168060447813773548586650370526201455642541757...

On remarque que le produit du nombre de périodes (2) et de leurs longueurs (53) est égal à 106 et donc au premier -1.