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

 

Be sure to include complete explanations with your answer, using complete sentences. Imagine you were going to show your solution to a classmate, and try to write your solution so that they could understand it without doing any extra work.

 Jul 18, 2024
 #1
avatar+1926 
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Let's first take a look at the fraction 1/17. 

It has 16 repeating digits in the form of \(0. \overline{0588235294117647}\)

 

We simplfy have to find which digit the 4000th lies on. 

 

First, let's do 4000/16. 

We get \(4000/16=250\)

 

So the 4000th digit is the last digit of the repeating decimal, which is 7. 

 

So 7 is our answer. 

 

Thanks! :)

 Jul 18, 2024
edited by NotThatSmart  Jul 18, 2024

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