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

 Dec 8, 2024

Best Answer 

 #1
avatar+1953 
+1

Let's note that 1/17 is a repeating decimal. 

1/17=0.¯0588235294117647

 

There are 16 repeating digits in the decimal. 

Dividing 4000 by 16, we get

 

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! :)

 Dec 9, 2024
edited by NotThatSmart  Dec 9, 2024
 #1
avatar+1953 
+1
Best Answer

Let's note that 1/17 is a repeating decimal. 

 

There are 16 repeating digits in the decimal. 

Dividing 4000 by 16, we get

 

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! :)

NotThatSmart Dec 9, 2024
edited by NotThatSmart  Dec 9, 2024

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