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Find the $4000$th digit following the decimal point in the expansion of $\frac{1}{17}$

 Jul 24, 2024
 #1
avatar+1858 
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Let's note that 1/17 is a repeating decimal. 

\(1/17 = 0.\overline{ 0588235294117647}\)

 

There are 16 repeating digits in the decimal. 

Dividing 4000 by 16, we get

\(4000/16 = 250\)

Since it is divisble, then we can conclude that the last digit of the repeating decimal is the correct answer. 

Thus, 7 is the final answer. 

 

Thanks! :)

 Jul 24, 2024
edited by NotThatSmart  Jul 24, 2024

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