Question #b5604
1 Answer
Feb 24, 2017
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#