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avatar+1314 

What is the product of the numerator and the denominator when $0.\overline{009}$ is expressed as a fraction in lowest terms?

 May 25, 2015

Best Answer 

 #5
avatar+1314 
+7

dunno....look at his awnser

 May 25, 2015
 #1
avatar+4711 
+5

I think...

 

0.009 as a fraction is 9/10000 ....

That's it simplified.....

 

9*10000=90,000

 

Your answer is 90,000

 May 25, 2015
 #2
avatar+129852 
+6

.009009009  =   9/999  = 1/111

 

And 1 * 111 =   111

 

 

 May 25, 2015
 #3
avatar+4711 
+5

What did I do wrong?

 May 25, 2015
 #4
avatar+1314 
+5

tanks u(thank you

 May 25, 2015
 #5
avatar+1314 
+7
Best Answer

dunno....look at his awnser

AWESOMEEE May 25, 2015
 #6
avatar+129852 
+6

The "bar" over the .009 indicates that this part repeats.....  so.....we have .009009009009.....etc. .....and we can write this as  9 / [ a number having the same number of 9's as the number of digits in the repeating cycle length ]

 

And notice that we have 3 digits in the repeating cycle length......so the denominator of the above fraction is just 999.......

 

 

 May 25, 2015

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