Question

How do you convert 3/11 to a decimal?

Answer 1

`3/11=0.272727...............`

Explanation:

`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...............`