Express the recurring decimal 0.1576(bar on 576) as a rational no. Using concept of infinite geometric series.? Share with your friends Share 1 Aman Choubey answered this Dear Student, 0.1576=0.1576576576......=0.1+0.0576+0.0000576+0.0000000576+.......=0.1+57610000+57610000000+.....Since the repeating pattern is an infinite converging geometric series whose ratio of successive term is less than 1 i.e. r=0.001 then we can use sum of infinite geometric series S∞=a11-r 0.1576=0.1+576100001-11000=110+576100009991000=110+5769990=999+5769990=15759990Regards. 5 View Full Answer
