Question

Xpress 8.54545454545... as a rational number, in the form pq where p and q are positive integers with no common factors.

Answer 1

If you mean p/q, then this is how you do it:

$\textrm{Let x represent the recurring decimal.}\\x = 8.54545...\\100x = 854.54545...\\\textrm{Subtract first expression from second expression.}\\100x - x = 99x\\854.54545... - 8.54545... = 846\\\therefore 99x = 846\\\textrm{Isolate x term by dividing by 99 on both sides of the expression.}\\x = 846\div99$

$x = \frac{846}{99} = \frac{94}{11}$

Therefore your final answer is 94/11, where p is 94 and q is 11.