Write 0.87 repeating as a fraction in simplest form

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

Which is fraction in simplest form.