what is 8.26666667 in simplest form

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14-03-2018
Mathematics

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what is 8.26666667 in simplest form

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JonHenderson55 JonHenderson55 · Answer 1 · 2018-03-14T06:18:32+01:00

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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