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 A Golden Fraction (Posted on 2019-03-12)
What is the 250th digit to the right of the decimal place of the fraction below?

100,000,000,000,000,000,000
----------------------------------
99,999,999,989,999,999,999

 No Solution Yet Submitted by Danish Ahmed Khan No Rating

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 UBASIC solution (spoiler) | Comment 1 of 2
5   point 222
10   F=100000000000000000000/99999999989999999999
20   open "goldfrac.txt" for output as #2
30    Print #2,F
40   close #2

I've grouped the output by 50's after the decimal point:

` 1.00000000010000000002000000000300000000050000000008  (50)   00000000130000000021000000003400000000550000000089 (100)   00000001440000000233000000037700000006100000000987  ...    00000015970000002584000000418100000067650000010946   00000177110000028657000004636800000750250000121393 (250)   00001964180000317811000051422900008320400001346269   00021783090003524578000570288700092274650014930352   00241578170039088169006324598601023341550165580141   02679142960433494437070140873311349031701836311903   29712150734807526976777874205025862690270365011077   29512801043316291181626757128595838624675851433753   54352962211286729974672202619580087561704730782366   27395385367470320903020985943976801803427890039782   55702201253460259907903048003324907399411521219974   40119599155533179889954513980550783196954623459500   97017791964325238697402701789383522565912379274485   07315310763110805561384233663769531421990795478836   77486210358544099872629272090848368207811129541689   59663624707095904160306226663101581707913220437422   33786082136599045635997765384965766994856554353335   31310528209685406156281645897725018651335318324110   7820189244313851335 `

The digit is a 3 and in fact is the last digit of the 25th Fibonacci number (counting 1 and 2 as the first and second Fibonacci numbers -- 26th counting 1 and 1 as the first and second -- in fact the first 1 is to the left of the decimal point), as groups of 10 digits seem to represent Fibonacci numbers until overflow causes them to overlap.

 Posted by Charlie on 2019-03-12 15:51:27

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