Il existe 4 périodes de 24 chiffres pour n/97 en base 9.

Pour toutes les fractions de n/97 en base 9, la période de 1/97 revient alors 24 fois (en orange)

1/97=0,007456685583881432203305...

2/97=0,016024482277872864406611...

3/97=0,024482277872864406611016...

4/97=0,033050074566855838814322...

5/97=0,041516771261847372117627...

6/97=0,050074566855838814322033...

7/97=0,057542363550831346525338...

8/97=0,066110160244822778728644...

9/97=0,074566855838814322033050...

10/97=0,083134652533805754236355...

11/97=0,101602448227787286440661...

12/97=0,110160244822778728644066...

13/97=0,117627041516771261847372...

14/97=0,126184737211762704151677...

15/97=0,134652533805754236355083...

16/97=0,143220330500745668558388...

17/97=0,151677126184737211762704...

18/97=0,160244822778728644066110...

19/97=0,167712618473721176270415...

20/97=0,176270415167712618473721...

21/97=0,184737211762704151677126...

22/97=0,203305007456685583881432...

23/97=0,211762704151677126184737...

24/97=0,220330500745668558388143...

25/97=0,227787286440661101602448...

26/97=0,236355083134652533805754...

27/97=0,244822778728644066110160...

28/97=0,253380575423635508313465...

29/97=0,261847372117627041516771...

30/97=0,270415167712618473721176...

31/97=0,277872864406611016024482...

32/97=0,286440661101602448227787...

33/97=0,305007456685583881432203...

34/97=0,313465253380575423635508...

35/97=0,322033050074566855838814...

36/97=0,330500745668558388143220...

37/97=0,338057542363550831346525...

38/97=0,346525338057542363550831...

39/97=0,355083134652533805754236...

40/97=0,363550831346525338057542...

41/97=0,372117627041516771261847...

42/97=0,380575423635508313465253...

43/97=0,388143220330500745668558...

44/97=0,406611016024482277872864...

45/97=0,415167712618473721176270...

46/97=0,423635508313465253380575...

47/97=0,432203305007456685583881...

48/97=0,440661101602448227787286...

49/97=0,448227787286440661101602...

50/97=0,456685583881432203305007...

51/97=0,465253380575423635508313...

52/97=0,473721176270415167712618...

53/97=0,482277872864406611016024...

54/97=0,500745668558388143220330...

55/97=0,508313465253380575423635...

56/97=0,516771261847372117627041...

57/97=0,525338057542363550831346...

58/97=0,533805754236355083134652...

59/97=0,542363550831346525338057...

60/97=0,550831346525338057542363...

61/97=0,558388143220330500745668...

62/97=0,566855838814322033050074...

63/97=0,575423635508313465253380...

64/97=0,583881432203305007456685...

65/97=0,602448227787286440661101...

66/97=0,611016024482277872864406...

67/97=0,618473721176270415167712...

68/97=0,627041516771261847372117...

69/97=0,635508313465253380575423...

70/97=0,644066110160244822778728...

71/97=0,652533805754236355083134...

72/97=0,661101602448227787286440...

73/97=0,668558388143220330500745...

74/97=0,677126184737211762704151...

75/97=0,685583881432203305007456...

76/97=0,704151677126184737211762...

77/97=0,712618473721176270415167...

78/97=0,721176270415167712618473...

79/97=0,728644066110160244822778...

80/97=0,737211762704151677126184...

81/97=0,745668558388143220330500...

82/97=0,754236355083134652533805...

83/97=0,762704151677126184737211...

84/97=0,771261847372117627041516...

85/97=0,778728644066110160244822...

86/97=0,787286440661101602448227...

87/97=0,805754236355083134652533...

88/97=0,814322033050074566855838...

89/97=0,822778728644066110160244...

90/97=0,831346525338057542363550...

91/97=0,838814322033050074566855...

92/97=0,847372117627041516771261...

93/97=0,855838814322033050074566...

94/97=0,864406611016024482277872...

95/97=0,872864406611016024482277...

96/97=0,881432203305007456685583...

On remarque que le produit du nombre de périodes (4) et de leurs longueurs (24) est égal à 96 et donc au premier -1.