How do you convert 3/11 to a decimal?

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Answer 1 · 2016-06-18T06:37:25

$3/11=0.272727...............$

$3/11$

= $30/11xx(1/10)$

= $(22+8)/11xx1/10$

= $22/11xx1/10+8/11xx1/10$

= $(2xx1)/10+80/11xx1/100$

= $2/10+(77+3)/11xx1/100$

= $2/10+77/11xx1/100+3/11xx1/100$ or

$3/11=2/10+7/100+1/100xx(3/11)$ ........(A)

Now using value of $3/11$ from (A) within (A)

$3/11=2/10+7/100+1/100xx(2/10+7/100+1/100xx(3/11))$

= $2/10+7/100+2/1000+7/10000+1/10000xx(3/11))$

Now, if we keep on repeating this endlessly

$3/11=2/10+7/100+2/1000+7/10000+2/100000+7/1000000+......$

or $3/11=0.272727...............$