base 4: 0.42611111111111106576455... = [0;2,2,1,7,1,1,2,1,1,1,1,6806293849,1,33,157,1,2,1...] convergents: 0,1/2,2/5,3/7,23/54,26/61,49/115,124/291,173/406,297/697,470/1103,767/1800, ... 767/1800 = 0.4261 so is correct to 15 dps.
base 5: 0.3107361111111111111111111111109630333... = [0;3,4,1,1,2,2,18,1,20,1302701925685142513155, ...] convergents: 0,1/3,4/13,5/16,9/29,23/74,55/177,1013/3260,1068/3437,22373/72000, ... 22373/72000 = 0.3107361 correct to 29 dps (44 base 5 places) with the next convergent being accurate to 51 dps or 75 base 6 digits.
base 6: 0.2398626858150667674477198286722096245905769715293502137... = [0;4,5,1,10,1,4,3,9,1,2,2,1,1,699745284439054751106354294914368414245,...] convergents: 0,1/4,5/21,6/25,65/271,71/296,349/1455,1118/4661,10411/43404,11529/48065,33469/139534,78467/327133,111936/466667,190403/793800,133233601393049341774903176814580489177602671/555457806787721661428224039303025647228147667 190403/793800 = 0.23986268581506676744771982867220962459057697152935248173... correct to 49 dps (65 places in base 6). The next convergent increases the accuracy to 88 dps or 115 base 6 digits!