Respuesta :

JonHenderson55
The answer is:  " 8 [tex] \frac{4}{15} [/tex] " .
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Explanation:
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Given: "8.266666667 " ;  write in "simplest form" ; 
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Let us assume that the number is meant to be:  

"8.2666666.. " (with repeating "6's) .

Consider the:  "0.26666666666...." ; 

Let "x = 0.26666666666...." ; 

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100x = 26.666666666666666666................... ;

10x =  2.666666666666666666....................... ; 

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Note:  " 100x – 10x = 90x " ; 

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   100x  =  26.666666666666666666................... 

–   10x  =    2.666666666666666666....................... 

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    90x  = 24.00000000000000000.........................

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   →  90x = 24 ; 

Divide each side of the equation by "90" ; 

   →  90x / 90 = 24/90 ; 

to get:

→  x = 24/90 ; 

→  x = 24/90 = (24÷6) / (90÷6) = 4/15 ; 


Add the "whole number, " 8 "; to this value; to get:

→  " 8 [tex] \frac{4}{15} [/tex] " .

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