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avatar+764 

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 3, 2024
 #1
avatar+867 
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The 4000th digit is 2.

 Jul 3, 2024
 #2
avatar+1256 
+1

First, let's note that 1/17 is a repeating decimal. 

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

 

There are 16 repeating digits. 

Thus, we do 4000/16. We get

\(4000/16=250\)

 

Since it's divisible, it means the last digit of the repeating part is our answer, which is 7. 

 

So 7 is our answer. 

 

Thanks! :)

 Jul 3, 2024

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