In veronica’s art class 5 out of 9 people speak spanish. what decimal number shows what part of the class speaks spanish?

The answer is:  " 0.55555555555555 " .

Note:

 " 5 out of 9" = 5/9 = (5*10) / (9*10) = 50/90; 

Divide side by "9" :

(50÷9) / (90÷9) ;
 
  (5.555555555555555... ) / (10) =


" 0.55555555555555 "


Note:  To check our answer; consider the "reverse order" of the problem:

"Write the decimal number, "0.5 (with a repeating bar over the "5")"  ;  as a fraction:

Let x = 0.555555555555555 ; 

10x = 5.555555555555555555" ; 

Note:  We consider "10x" ;  since, the number of "decimals being repeated" ends in the "tenths" place.

  So: 


    10x = 5.55555555555555555555555555555555
–     x = 0.55555555555555555555555555555555

     9x = 5.0000000000000000000000000000000 ;


    →  9x = 5 ;

Divide EACH SIDE of the equation by "9" ; 
  to isolate "x" on one side of the equation; & to solve for "x" :

   →  9x / 9  = 5 / 9 ; 

to get: 

x =  5/9  ;  which is "5 out of 9" .

The answer makes sense!

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