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Let $x = (0.\overline{6})(0.\overline{06})$.  When x is written out as a decimal, what is the sum of the first 15 digits after the decimal point?

 Apr 2, 2021
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$(0.\overline{6})(0.\overline{06})=(6/9)*(6/99)=4/99=0.\overline{04}$

 

The sum of the first $15$ digits will be $0+4+0+4+0+4...+4+0$. This has length $15$, with $8$ zeroes and $7$ fours. So it is equal to $8(0)+7(4)=\boxed{28}$

 Apr 2, 2021

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