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What numeral is in the 100th decimal place in the decimal representation of \(6/11\)?

 Jan 16, 2022
 #1
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What numeral is in the 100th decimal place in the decimal representation of 6/11?  

 

This is a repeating decimal.  It goes  

 

0.54 54 54 54 54 54 54 54 54 54  

   54 54 54 54 54 54 54 54 54 54  

   54 54 54 54 54 54 54 54 54 54  

   54 54 54 54 54 54 54 54 54 54  

   54 54 54 54 54 54 54 54 54 54  

   54 54 54 54 54 54 54 54 54 54  

   54 54 54 54 54 54 54 54 54 54  

   54 54 54 54 54 54 54 54 54 54  

   54 54 54 54 54 54 54 54 54 54  

   54 54 54 54 54 54 54 54 54 54  

 

It's a 4.   

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 Jan 16, 2022
 #2
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instead of writing all the 54's(which is in fact very painful!) since 54 is even and 100 is even, 4 must be the 100th digit

 Jan 16, 2022
 #3
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You're right, but it wasn't necessary to write them all painfully. 

Since it repeats, I wrote one line then copied and pasted the rest.  

If you notice, I actually went to the 200th digit.  Buy 100, get 100 free. 

.

Guest Jan 16, 2022

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