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What numeral is in the 100th decimal place in the decimal representation of $\frac{6}{7}$?

 Jun 27, 2020
 #1
avatar+643 
+2

\(\frac{6}{7}=0.\overline{857142}\)

 

The six digits 857142 repeat. We divide 100 by 6 to get 16 r 4. The 6 digits are repeated only 16 times. The remaining four are not. The fourth number in this group is 1.

 

Edit: Oops somehow I got a two.

 Jun 27, 2020
edited by gwenspooner85  Jun 27, 2020
 #2
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+1

6 / 7 = 0.8571428571 4285714285 7142857142 8571428571 4285714285 7142857142 8571428571 4285714285 7142857142 8571428571 - The 100th decimal digit is 1.

 Jun 27, 2020
 #3
avatar+110233 
+1

6/7 = 0.8571428571428571......

 

0.857142 85........

1 is 8

7 is  8

1+6n will be 8

1+6*16 = 97th will be 8

98th         5

99th          7

 

100th     will be 1

 Jun 27, 2020

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