Il existe 2 périodes de 98 chiffres pour n/197 en base 10.

Pour toutes les fractions de n/197 en base 10, la période de 1/197 revient alors 98 fois (en orange)

1/197=0,00507614213197969543147208121827411167512690355329949238578680203045685279187817258883248730964467...

2/197=0,01015228426395939086294416243654822335025380710659898477157360406091370558375634517766497461928934...

3/197=0,01522842639593908629441624365482233502538071065989847715736040609137055837563451776649746192893401...

4/197=0,02030456852791878172588832487309644670050761421319796954314720812182741116751269035532994923857868...

5/197=0,02538071065989847715736040609137055837563451776649746192893401015228426395939086294416243654822335...

6/197=0,03045685279187817258883248730964467005076142131979695431472081218274111675126903553299492385786802...

7/197=0,03553299492385786802030456852791878172588832487309644670050761421319796954314720812182741116751269...

8/197=0,04060913705583756345177664974619289340101522842639593908629441624365482233502538071065989847715736...

9/197=0,04568527918781725888324873096446700507614213197969543147208121827411167512690355329949238578680203...

10/197=0,05076142131979695431472081218274111675126903553299492385786802030456852791878172588832487309644670...

11/197=0,05583756345177664974619289340101522842639593908629441624365482233502538071065989847715736040609137...

12/197=0,06091370558375634517766497461928934010152284263959390862944162436548223350253807106598984771573604...

13/197=0,06598984771573604060913705583756345177664974619289340101522842639593908629441624365482233502538071...

14/197=0,07106598984771573604060913705583756345177664974619289340101522842639593908629441624365482233502538...

15/197=0,07614213197969543147208121827411167512690355329949238578680203045685279187817258883248730964467005...

16/197=0,08121827411167512690355329949238578680203045685279187817258883248730964467005076142131979695431472...

17/197=0,08629441624365482233502538071065989847715736040609137055837563451776649746192893401015228426395939...

18/197=0,09137055837563451776649746192893401015228426395939086294416243654822335025380710659898477157360406...

19/197=0,09644670050761421319796954314720812182741116751269035532994923857868020304568527918781725888324873...

20/197=0,10152284263959390862944162436548223350253807106598984771573604060913705583756345177664974619289340...

21/197=0,10659898477157360406091370558375634517766497461928934010152284263959390862944162436548223350253807...

22/197=0,11167512690355329949238578680203045685279187817258883248730964467005076142131979695431472081218274...

23/197=0,11675126903553299492385786802030456852791878172588832487309644670050761421319796954314720812182741...

24/197=0,12182741116751269035532994923857868020304568527918781725888324873096446700507614213197969543147208...

25/197=0,12690355329949238578680203045685279187817258883248730964467005076142131979695431472081218274111675...

26/197=0,13197969543147208121827411167512690355329949238578680203045685279187817258883248730964467005076142...

27/197=0,13705583756345177664974619289340101522842639593908629441624365482233502538071065989847715736040609...

28/197=0,14213197969543147208121827411167512690355329949238578680203045685279187817258883248730964467005076...

29/197=0,14720812182741116751269035532994923857868020304568527918781725888324873096446700507614213197969543...

30/197=0,15228426395939086294416243654822335025380710659898477157360406091370558375634517766497461928934010...

31/197=0,15736040609137055837563451776649746192893401015228426395939086294416243654822335025380710659898477...

32/197=0,16243654822335025380710659898477157360406091370558375634517766497461928934010152284263959390862944...

33/197=0,16751269035532994923857868020304568527918781725888324873096446700507614213197969543147208121827411...

34/197=0,17258883248730964467005076142131979695431472081218274111675126903553299492385786802030456852791878...

35/197=0,17766497461928934010152284263959390862944162436548223350253807106598984771573604060913705583756345...

36/197=0,18274111675126903553299492385786802030456852791878172588832487309644670050761421319796954314720812...

37/197=0,18781725888324873096446700507614213197969543147208121827411167512690355329949238578680203045685279...

38/197=0,19289340101522842639593908629441624365482233502538071065989847715736040609137055837563451776649746...

39/197=0,19796954314720812182741116751269035532994923857868020304568527918781725888324873096446700507614213...

40/197=0,20304568527918781725888324873096446700507614213197969543147208121827411167512690355329949238578680...

41/197=0,20812182741116751269035532994923857868020304568527918781725888324873096446700507614213197969543147...

42/197=0,21319796954314720812182741116751269035532994923857868020304568527918781725888324873096446700507614...

43/197=0,21827411167512690355329949238578680203045685279187817258883248730964467005076142131979695431472081...

44/197=0,22335025380710659898477157360406091370558375634517766497461928934010152284263959390862944162436548...

45/197=0,22842639593908629441624365482233502538071065989847715736040609137055837563451776649746192893401015...

46/197=0,23350253807106598984771573604060913705583756345177664974619289340101522842639593908629441624365482...

47/197=0,23857868020304568527918781725888324873096446700507614213197969543147208121827411167512690355329949...

48/197=0,24365482233502538071065989847715736040609137055837563451776649746192893401015228426395939086294416...

49/197=0,24873096446700507614213197969543147208121827411167512690355329949238578680203045685279187817258883...

50/197=0,25380710659898477157360406091370558375634517766497461928934010152284263959390862944162436548223350...

51/197=0,25888324873096446700507614213197969543147208121827411167512690355329949238578680203045685279187817...

52/197=0,26395939086294416243654822335025380710659898477157360406091370558375634517766497461928934010152284...

53/197=0,26903553299492385786802030456852791878172588832487309644670050761421319796954314720812182741116751...

54/197=0,27411167512690355329949238578680203045685279187817258883248730964467005076142131979695431472081218...

55/197=0,27918781725888324873096446700507614213197969543147208121827411167512690355329949238578680203045685...

56/197=0,28426395939086294416243654822335025380710659898477157360406091370558375634517766497461928934010152...

57/197=0,28934010152284263959390862944162436548223350253807106598984771573604060913705583756345177664974619...

58/197=0,29441624365482233502538071065989847715736040609137055837563451776649746192893401015228426395939086...

59/197=0,29949238578680203045685279187817258883248730964467005076142131979695431472081218274111675126903553...

60/197=0,30456852791878172588832487309644670050761421319796954314720812182741116751269035532994923857868020...

61/197=0,30964467005076142131979695431472081218274111675126903553299492385786802030456852791878172588832487...

62/197=0,31472081218274111675126903553299492385786802030456852791878172588832487309644670050761421319796954...

63/197=0,31979695431472081218274111675126903553299492385786802030456852791878172588832487309644670050761421...

64/197=0,32487309644670050761421319796954314720812182741116751269035532994923857868020304568527918781725888...

65/197=0,32994923857868020304568527918781725888324873096446700507614213197969543147208121827411167512690355...

66/197=0,33502538071065989847715736040609137055837563451776649746192893401015228426395939086294416243654822...

67/197=0,34010152284263959390862944162436548223350253807106598984771573604060913705583756345177664974619289...

68/197=0,34517766497461928934010152284263959390862944162436548223350253807106598984771573604060913705583756...

69/197=0,35025380710659898477157360406091370558375634517766497461928934010152284263959390862944162436548223...

70/197=0,35532994923857868020304568527918781725888324873096446700507614213197969543147208121827411167512690...

71/197=0,36040609137055837563451776649746192893401015228426395939086294416243654822335025380710659898477157...

72/197=0,36548223350253807106598984771573604060913705583756345177664974619289340101522842639593908629441624...

73/197=0,37055837563451776649746192893401015228426395939086294416243654822335025380710659898477157360406091...

74/197=0,37563451776649746192893401015228426395939086294416243654822335025380710659898477157360406091370558...

75/197=0,38071065989847715736040609137055837563451776649746192893401015228426395939086294416243654822335025...

76/197=0,38578680203045685279187817258883248730964467005076142131979695431472081218274111675126903553299492...

77/197=0,39086294416243654822335025380710659898477157360406091370558375634517766497461928934010152284263959...

78/197=0,39593908629441624365482233502538071065989847715736040609137055837563451776649746192893401015228426...

79/197=0,40101522842639593908629441624365482233502538071065989847715736040609137055837563451776649746192893...

80/197=0,40609137055837563451776649746192893401015228426395939086294416243654822335025380710659898477157360...

81/197=0,41116751269035532994923857868020304568527918781725888324873096446700507614213197969543147208121827...

82/197=0,41624365482233502538071065989847715736040609137055837563451776649746192893401015228426395939086294...

83/197=0,42131979695431472081218274111675126903553299492385786802030456852791878172588832487309644670050761...

84/197=0,42639593908629441624365482233502538071065989847715736040609137055837563451776649746192893401015228...

85/197=0,43147208121827411167512690355329949238578680203045685279187817258883248730964467005076142131979695...

86/197=0,43654822335025380710659898477157360406091370558375634517766497461928934010152284263959390862944162...

87/197=0,44162436548223350253807106598984771573604060913705583756345177664974619289340101522842639593908629...

88/197=0,44670050761421319796954314720812182741116751269035532994923857868020304568527918781725888324873096...

89/197=0,45177664974619289340101522842639593908629441624365482233502538071065989847715736040609137055837563...

90/197=0,45685279187817258883248730964467005076142131979695431472081218274111675126903553299492385786802030...

91/197=0,46192893401015228426395939086294416243654822335025380710659898477157360406091370558375634517766497...

92/197=0,46700507614213197969543147208121827411167512690355329949238578680203045685279187817258883248730964...

93/197=0,47208121827411167512690355329949238578680203045685279187817258883248730964467005076142131979695431...

94/197=0,47715736040609137055837563451776649746192893401015228426395939086294416243654822335025380710659898...

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100/197=0,50761421319796954314720812182741116751269035532994923857868020304568527918781725888324873096446700...

101/197=0,51269035532994923857868020304568527918781725888324873096446700507614213197969543147208121827411167...

102/197=0,51776649746192893401015228426395939086294416243654822335025380710659898477157360406091370558375634...

103/197=0,52284263959390862944162436548223350253807106598984771573604060913705583756345177664974619289340101...

104/197=0,52791878172588832487309644670050761421319796954314720812182741116751269035532994923857868020304568...

105/197=0,53299492385786802030456852791878172588832487309644670050761421319796954314720812182741116751269035...

106/197=0,53807106598984771573604060913705583756345177664974619289340101522842639593908629441624365482233502...

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108/197=0,54822335025380710659898477157360406091370558375634517766497461928934010152284263959390862944162436...

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110/197=0,55837563451776649746192893401015228426395939086294416243654822335025380710659898477157360406091370...

111/197=0,56345177664974619289340101522842639593908629441624365482233502538071065989847715736040609137055837...

112/197=0,56852791878172588832487309644670050761421319796954314720812182741116751269035532994923857868020304...

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118/197=0,59898477157360406091370558375634517766497461928934010152284263959390862944162436548223350253807106...

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120/197=0,60913705583756345177664974619289340101522842639593908629441624365482233502538071065989847715736040...

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157/197=0,79695431472081218274111675126903553299492385786802030456852791878172588832487309644670050761421319...

158/197=0,80203045685279187817258883248730964467005076142131979695431472081218274111675126903553299492385786...

159/197=0,80710659898477157360406091370558375634517766497461928934010152284263959390862944162436548223350253...

160/197=0,81218274111675126903553299492385786802030456852791878172588832487309644670050761421319796954314720...

161/197=0,81725888324873096446700507614213197969543147208121827411167512690355329949238578680203045685279187...

162/197=0,82233502538071065989847715736040609137055837563451776649746192893401015228426395939086294416243654...

163/197=0,82741116751269035532994923857868020304568527918781725888324873096446700507614213197969543147208121...

164/197=0,83248730964467005076142131979695431472081218274111675126903553299492385786802030456852791878172588...

165/197=0,83756345177664974619289340101522842639593908629441624365482233502538071065989847715736040609137055...

166/197=0,84263959390862944162436548223350253807106598984771573604060913705583756345177664974619289340101522...

167/197=0,84771573604060913705583756345177664974619289340101522842639593908629441624365482233502538071065989...

168/197=0,85279187817258883248730964467005076142131979695431472081218274111675126903553299492385786802030456...

169/197=0,85786802030456852791878172588832487309644670050761421319796954314720812182741116751269035532994923...

170/197=0,86294416243654822335025380710659898477157360406091370558375634517766497461928934010152284263959390...

171/197=0,86802030456852791878172588832487309644670050761421319796954314720812182741116751269035532994923857...

172/197=0,87309644670050761421319796954314720812182741116751269035532994923857868020304568527918781725888324...

173/197=0,87817258883248730964467005076142131979695431472081218274111675126903553299492385786802030456852791...

174/197=0,88324873096446700507614213197969543147208121827411167512690355329949238578680203045685279187817258...

175/197=0,88832487309644670050761421319796954314720812182741116751269035532994923857868020304568527918781725...

176/197=0,89340101522842639593908629441624365482233502538071065989847715736040609137055837563451776649746192...

177/197=0,89847715736040609137055837563451776649746192893401015228426395939086294416243654822335025380710659...

178/197=0,90355329949238578680203045685279187817258883248730964467005076142131979695431472081218274111675126...

179/197=0,90862944162436548223350253807106598984771573604060913705583756345177664974619289340101522842639593...

180/197=0,91370558375634517766497461928934010152284263959390862944162436548223350253807106598984771573604060...

181/197=0,91878172588832487309644670050761421319796954314720812182741116751269035532994923857868020304568527...

182/197=0,92385786802030456852791878172588832487309644670050761421319796954314720812182741116751269035532994...

183/197=0,92893401015228426395939086294416243654822335025380710659898477157360406091370558375634517766497461...

184/197=0,93401015228426395939086294416243654822335025380710659898477157360406091370558375634517766497461928...

185/197=0,93908629441624365482233502538071065989847715736040609137055837563451776649746192893401015228426395...

186/197=0,94416243654822335025380710659898477157360406091370558375634517766497461928934010152284263959390862...

187/197=0,94923857868020304568527918781725888324873096446700507614213197969543147208121827411167512690355329...

188/197=0,95431472081218274111675126903553299492385786802030456852791878172588832487309644670050761421319796...

189/197=0,95939086294416243654822335025380710659898477157360406091370558375634517766497461928934010152284263...

190/197=0,96446700507614213197969543147208121827411167512690355329949238578680203045685279187817258883248730...

191/197=0,96954314720812182741116751269035532994923857868020304568527918781725888324873096446700507614213197...

192/197=0,97461928934010152284263959390862944162436548223350253807106598984771573604060913705583756345177664...

193/197=0,97969543147208121827411167512690355329949238578680203045685279187817258883248730964467005076142131...

194/197=0,98477157360406091370558375634517766497461928934010152284263959390862944162436548223350253807106598...

195/197=0,98984771573604060913705583756345177664974619289340101522842639593908629441624365482233502538071065...

196/197=0,99492385786802030456852791878172588832487309644670050761421319796954314720812182741116751269035532...

On remarque que le produit du nombre de périodes (2) et de leurs longueurs (98) est égal à 196 et donc au premier -1.