The answer is: " 0.55555555555555...... " .
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Note:
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" 5 out of 9" = 5/9 = (5*10) / (9*10) = 50/90;
Divide side by "9" :
(50÷9) / (90÷9) ;
(5.555555555555555... ) / (10) =
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" 0.55555555555555...... "
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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.
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So:
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10x = 5.55555555555555555555555555555555.......................
– x = 0.55555555555555555555555555555555.......................
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9x = 5.0000000000000000000000000000000...................... ;
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→ 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" .
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The answer makes sense!
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