Question #b5604

1 Answer
Feb 24, 2017

#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#