Express \(0.5\overline{10}\) as a common fraction.
Let x = 0.51010101010....
10x = 5.1010101010....
1000x = 510.1010101010....
1000x - 10 x = 505
990x = 505
x = 505/990 = 101/198
we know that 0.5=1/2 and this is 0.0101010... more than 1/2 and we know that 100/199=0.502512563...,101/199=0.507537688,102/199=0.512562814... so 0.5101010... is in between 101/199 and 102/199 so we have that 0.5101010... is 101/198
