1. ## P/q?

The problem states:
Express 5.2727... as a rational number in the form of p/q where p and q are positive integers with no common factors.
The only way I know how to solve is to keep plugging number in the calculator until I find that number...I found the answer to be 61 for p and 11 for q, but I don't actually know how to do it.

Can you explain this to me?

2. Originally Posted by Bracketology
The problem states:
Express 5.2727... as a rational number in the form of p/q where p and q are positive integers with no common factors.
The only way I know how to solve is to keep plugging number in the calculator until I find that number...I found the answer to be 61 for p and 11 for q, but I don't actually know how to do it.

Can you explain this to me?
Let x denote the number $5.\overline{27}$

Then

$\begin{array}{rcr}100x&=&527.\overline{27} \\ x&=&5.\overline{27}\end{array}$

Subtract columnwise and you'll get:

$99x = 522~\implies~x=\dfrac{522}{99}=\dfrac{58}{11}$

Btw: $\dfrac{61}{11} = 5.\overline{54}$

3. oops, should have said 58/11. Yea, I got the answer in the calculator. Thanks for the help.