+0  
 
0
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avatar+232 

Subtract \(0.\overline{07}\) from 0.07 and convert the answer to a simplified fraction.

 Dec 19, 2019
 #1
avatar+88 
+2

This is just 7/99 - 7/100, or 7/9900.

 

~~GF

 Dec 19, 2019
 #2
avatar+111321 
+1

To convert  .07 (repeating) to  a fraction

 

Let   x  = .07  (repeating)

Multiply both sides   by  100

100x  =  7.07 (repeating)

 

100x  - x     =   7.07(repeating)  -  .07(repeating)

99x  =  7

x  = 7/99

 

So

 

.07 -  .07 (repeating)  =

 

7/100  -  7/99  =

 

7(99) - 7(100)

___________   = 

100 *  99

 

7 (99 - 100)

__________   = 

     9900

 

7 (-1)

______   =

  9900

 

   -7 

_____

 9900

 

 

cool cool cool

 Dec 19, 2019
edited by CPhill  Dec 19, 2019

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