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

 Feb 17, 2020
 #1
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1 / 175 =0.0057142857............................AND ENDS IN..........142857. 7 is 4000th decimal digit.

 Feb 17, 2020
 #2
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Refer to here: https://web2.0calc.com/questions/what-is-the-4000th-digit-following-the-decimal-point-in-the-expansion-of-nbsp.

 

If you don't have time to click the link (which you should), this is what CPhill said: 

 

 

Notice the pattern........

 

1/175  = 0.0057142857142857........

 

There is a repeated cycle of 6 digits.......

 

2 leading zeroes + 666 cycles of 6 digits = 3998 digits......so ......two more digits will give us 4000......and the second digit in the pattern is "7".....so.......this is the 4000th digit........!!!

 Feb 17, 2020

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