12 REPORT 1877. 



It may be sometimes useful to have the values of Bernoulli's numbers expressed 

 in integers and repeating decimals. 



It readily follows from Staudt's theorem that if the fractional part of the wth 

 number of Bernoulli be converted into a repeating decimal, then the number of 

 figures in the repeating part will be either 2n or a divisor of 2», and the first figure 

 of the repeating part will occupy the second place of decimals. 



Table of Bernoulli's Numbers expressed in Integers and Bepeating Decimals. 



Ko. 



i -i6 



2 '03 



3 '02380 95 



4 -03 



5 075 



6 -25311 35 



7 1 16 



8 7-09215 68627 45 9 8 03 



9 54-97H7 7944 8 62155 3884 



10 579 -124 



11 6192-12318 84057 97101 44927 536 



12 86580-25311 35 



13 1* 25517-16 



14 272 98231 -06781 60919 54022 98850 57471 2643 



15 6015 80873 "90064 23683 84303 86817 48359 16771 4 



16 1 51163 15767-09215 68627 45098 03 



17 42 96146 43061 -16 



18 1371 16552 05088-33277 21590 87948 5616 



19 48833 23189 73593 -16 



20 19 29657 93419 40068 -14863 26681 4 



21 841 69304 75736 82615-00055 37098 56035 43743 07862 67995 57032 11517 165 



22 40338 07185 40594 55413-07681 15942 02898 55072 463 



23 21 15074 86380 81991 60560-14539 00709 21985 81560 28368 79432 62411 34751 



77304 96 



24 1208 66265 22296 52593 46027-31193 70825 25317 81943 54664 94290 02370 17884 24 



07670 7606 



25 75008 66746 07696 43668 55720 -075 25 



26 50 38778 10148 10689 14137 89303 -05220 12578 6163 26 



27 3652 87764 84818 12333 51104 30842-97117 79448 62155 3884 27 



28 2 84987 69302 45088 22262 69146 43291 -06781 60919 54022 98850 57471 2643 28 



29 238 65427 49968 36276 44645 98191 92192-14971 75141 24293 78531 07344 63276 29] 



83615 81920 90395 48022 59887 0056 



30 21399 949*5 72253 33 66 5 8l °74 47 6 5 J 9 I0 97 -39 a6 7 415 11 61723 87457 42183 30 



07692 65988 72659 15822 23522 99560 12610 6 



31 20 50097 57234 78097 56992 17330 95672 31025-16 31 



