Il existe 4 périodes de 25 chiffres pour n/101 en base 5.

Pour toutes les fractions de n/101 en base 5, la période de 1/101 revient alors 25 fois (en orange)

1/101=0,0011043224134234123140344...

2/101=0,0022142003324023301331243...

3/101=0,0033240233013312430022142...

4/101=0,0044334012203102103213041...

5/101=0,0110432241342341231403440...

6/101=0,0122031021032130410044334...

7/101=0,0133124300221420033240233...

8/101=0,0144223024411204211431132...

9/101=0,0210321304100443340122031...

10/101=0,0221420033240233013312430...

11/101=0,0233013312430022142003324...

12/101=0,0244112042114311320144223...

13/101=0,0310210321304100443340122...

14/101=0,0321304100443340122031021...

15/101=0,0332402330133124300221420...

16/101=0,0344001104322413423412314...

17/101=0,0410044334012203102103213...

18/101=0,0421143113201442230244112...

19/101=0,0432241342341231403440011...

20/101=0,0443340122031021032130410...

21/101=0,1004433401220310210321304...

22/101=0,1021032130410044334012203...

23/101=0,1032130410044334012203102...

24/101=0,1043224134234123140344001...

25/101=0,1104322413423412314034400...

26/101=0,1120421143113201442230244...

27/101=0,1132014422302441120421143...

28/101=0,1143113201442230244112042...

29/101=0,1204211431132014422302441...

30/101=0,1220310210321304100443340...

31/101=0,1231403440011043224134234...

32/101=0,1243002214200332402330133...

33/101=0,1304100443340122031021032...

34/101=0,1320144223024411204211431...

35/101=0,1331243002214200332402330...

36/101=0,1342341231403440011043224...

37/101=0,1403440011043224134234123...

38/101=0,1420033240233013312430022...

39/101=0,1431132014422302441120421...

40/101=0,1442230244112042114311320...

41/101=0,2003324023301331243002214...

42/101=0,2014422302441120421143113...

43/101=0,2031021032130410044334012...

44/101=0,2042114311320144223024411...

45/101=0,2103213041004433401220310...

46/101=0,2114311320144223024411204...

47/101=0,2130410044334012203102103...

48/101=0,2142003324023301331243002...

49/101=0,2203102103213041004433401...

50/101=0,2214200332402330133124300...

51/101=0,2230244112042114311320144...

52/101=0,2241342341231403440011043...

53/101=0,2302441120421143113201442...

54/101=0,2314034400110432241342341...

55/101=0,2330133124300221420033240...

56/101=0,2341231403440011043224134...

57/101=0,2402330133124300221420033...

58/101=0,2413423412314034400110432...

59/101=0,2430022142003324023301331...

60/101=0,2441120421143113201442230...

61/101=0,3002214200332402330133124...

62/101=0,3013312430022142003324023...

63/101=0,3024411204211431132014422...

64/101=0,3041004433401220310210321...

65/101=0,3102103213041004433401220...

66/101=0,3113201442230244112042114...

67/101=0,3124300221420033240233013...

68/101=0,3140344001104322413423412...

69/101=0,3201442230244112042114311...

70/101=0,3213041004433401220310210...

71/101=0,3224134234123140344001104...

72/101=0,3240233013312430022142003...

73/101=0,3301331243002214200332402...

74/101=0,3312430022142003324023301...

75/101=0,3324023301331243002214200...

76/101=0,3340122031021032130410044...

77/101=0,3401220310210321304100443...

78/101=0,3412314034400110432241342...

79/101=0,3423412314034400110432241...

80/101=0,3440011043224134234123140...

81/101=0,4001104322413423412314034...

82/101=0,4012203102103213041004433...

83/101=0,4023301331243002214200332...

84/101=0,4034400110432241342341231...

85/101=0,4100443340122031021032130...

86/101=0,4112042114311320144223024...

87/101=0,4123140344001104322413423...

88/101=0,4134234123140344001104322...

89/101=0,4200332402330133124300221...

90/101=0,4211431132014422302441120...

91/101=0,4223024411204211431132014...

92/101=0,4234123140344001104322413...

93/101=0,4300221420033240233013312...

94/101=0,4311320144223024411204211...

95/101=0,4322413423412314034400110...

96/101=0,4334012203102103213041004...

97/101=0,4400110432241342341231403...

98/101=0,4411204211431132014422302...

99/101=0,4422302441120421143113201...

100/101=0,4433401220310210321304100...

On remarque que le produit du nombre de périodes (4) et de leurs longueurs (25) est égal à 100 et donc au premier -1.