Let x = 0.99999......... ......(a)

We need to multiply both sides by 10 to get

10x = 9.9999...... ....(b)

We need to subtract (a) from (b). to get

We can also write 9 x = 9 as x = 9/9 or x = 1.

Therefore, on converting 0.99999.... in the p/q form, we get the answer as1.

Yes at a glance we are surprised at our answer. But the answer makes sense when we observe that 0.9999……… goes on forever. SO there is not gap between 1 and 0.9999……. and hence they are equal.