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Original Question
What is the 43rd digit after the decimal point in the decimal representation of 1/13?Asked by Anom
What is the 43rd digit after the decimal point in the decimal representation of 1/13?
Answers
Answered by
Reiny
1/13
= .076923076923076923...
notice the repeat is 076923 is 6 digits long
1st after decimal is 0
7th after the decimal is 0
13th after the decimal is 0
...
37th after the decimal is 0
43rd after the decimal is 0
notice that the numbers
1,7,13, ... 37, 43 all leave a remainder of 1 after dividing by 6, the length of my repeat
= .076923076923076923...
notice the repeat is 076923 is 6 digits long
1st after decimal is 0
7th after the decimal is 0
13th after the decimal is 0
...
37th after the decimal is 0
43rd after the decimal is 0
notice that the numbers
1,7,13, ... 37, 43 all leave a remainder of 1 after dividing by 6, the length of my repeat
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