x=0.878787.............. -----------(1)
Multiplying both sides by 100, we get,as the decimal repeats after two Hundreths
100 x=87.87878787............. -----------------------(2)
Subtracting (1) from (2) we get
100x-x=87.8787..... - 0.878787........
99 x=87
Dividing both sides by 99 we get
[tex]x=\frac{87}{99}\\\\=\frac{29}{33}[/tex]
Which is fraction in simplest form.
