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November 17th, 2016, 03:06 PM   #1
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The rational number 23949 divided by 99990 has the decimal representation expressed in what appears a non-periodic, plus a regular part:



0, 0023940239402394023940 ...



This decimal representation, the first digit 2 occupies the third decimal place and the first digit 9 occupies the fifth decimal place.

Watching these patterns of repetition, we conclude that the figure occupies the decimal 10 raised to the number 10 − 1 = 10000000000 − 1 is the digit? :furioso:
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November 17th, 2016, 03:14 PM   #2
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Quote:
Originally Posted by Samuel Leite View Post
The rational number 23949 divided by 99990 has the decimal representation expressed in what appears a non-periodic, plus a regular part:



0, 0023940239402394023940 ...



This decimal representation, the first digit 2 occupies the third decimal place and the first digit 9 occupies the fifth decimal place.

Watching these patterns of repetition, we conclude that the figure occupies the decimal 10 raised to the number 10 − 1 = 10000000000 − 1 is the digit? :furioso:
Are you asking what the 10^(10) - 1th decimal is?

Hint: You know the pattern 23940 is repeated every five spaces after the first two 0's. So what is the largest integer n such that 2 + 5n < 10^(10) - 1?

-Dan
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November 17th, 2016, 07:00 PM   #3
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My computer calculator gives a different result:

0.2395139513951395...
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