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Oh, and 169/1364 = 0.123900293255... and not 0.12390 :)
Well, 1.(9) = 2 and 0.123(9) is, in fact, equal to 0.124, while 0.12390 you suggested is 0.000(9) less :)
I think you don't really understand repeating decimals. Please refer to e.g. wikipedia: https://en.wikipedia.org/wiki/Repeating_decimal#Converting_repeating_decimals_to_fractions
ey.. why 1.(9) is 2 and 0.123(9) is 31/250 [is really 0.124]and not 169/1364 [is really 0.12390] that is closer
are these presicion problems? i though that you want to avoid them? base in the first problem of the serie
or there are tricky inputs