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 Let . When is written out as a decimal, what is the sum of the first digits after the decimal point?

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avatar+1310 

Let $x=(0.\overline{6})\cdot (0.\overline{60})$. When $x$ is written out as a decimal, what is the sum of the first $15$ digits after the decimal point?

 May 25, 2015

Best Answer 

 #1
avatar+128597 
+4

.666666.....   = 6/9  = 2/3

 

And  .606060.....  = 60/99

 

So

 

(2/3) (60/99)  =  (2/99)(60/3) = (2/99)(20) = 40/99 = .040404.........

 

So.......the sum of the first 15 digits  = 7(4) + 7(0) + 0 = 28

 

 

 May 25, 2015

3+0 Answers

 #1
avatar+128597 
+4
Best Answer

.666666.....   = 6/9  = 2/3

 

And  .606060.....  = 60/99

 

So

 

(2/3) (60/99)  =  (2/99)(60/3) = (2/99)(20) = 40/99 = .040404.........

 

So.......the sum of the first 15 digits  = 7(4) + 7(0) + 0 = 28

 

 

CPhill May 25, 2015
 #2
avatar+1310 
-1

its 32... sorry about that

 May 25, 2015
 #3
avatar
+1

Awesome if you knew the answer why did you ask cphill lol

 Feb 26, 2017

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