Question

Converting irrational recurring numbers to rational number

Answer 1

We can write 0.5¯¯¯0.5¯ as 0.55555555…0.55555555….

Let x=0.5¯¯¯,x=0.5¯, then

x=0.5+0.05+0.005+0.0005+⋯=510+5102+5103+5104+⋯=510×(1+110+1102+1103+⋯)=510×11−110=510×109=59.