Question

Question #b5604

Answer 1

`16/99`

Explanation:

We require to obtain 2 equations with the same repeating part after the decimal point and subtract them to eliminate the repeating part.

`"Note "0.bar(16)" represents "0.161616...`

`"let "x=0.bar(16)to(1)`

`rArr100x=16.bar(16)to(2)`

We now have the repeating part immediately after the decimal point in both equations and can subtract them.

`(2)-(1)" gives"`

`100x-x=16.bar(16)-0.bar(16)`

`rArr99x=16larr" repeating part eliminated"`

`rArrx=16/99`

`"Thus "0.bar(16)=16/99`