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

 Jun 17, 2024

Best Answer 

 #1
avatar+1250 
+1

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! :)

 Jun 17, 2024
 #1
avatar+1250 
+1
Best Answer

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! :)

NotThatSmart Jun 17, 2024

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