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What is the \({4000}^{th}\) digit following the decimal point in the expansion of \(1/175\)

 Dec 14, 2020
 #1
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1/175  is a    fraction with a repeating decimal  = . 00571428

 

Red part   is the repeating part

 

We can  solve this

 

2  +  6n   = 4000

 

6n =  4000  - 2

 

6n = 3998

 

n =  666  +  2/3

 

The  4000th digit  is  the second  interger in the  pattern   =   7

 

 

cool cool cool

 Dec 14, 2020

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