How do you express 7.545454... as a rational number p/q?

[Jade_punk181]

Homework Statement

Express 7.54545454545 . . . as a rational number, in the form p/q
where p and q are positive integers with no common factors.
p = ? and q = ?


This problem is nothing like I've seen before, so I don't even have a clue on how to start it.

 

[VeeEight]

There is a usual method of multiplying the number by 100 and subtracting and then dividing a few things to get a result (or tweaking it a little bit to fit your number). Have you seen this before? What methods have you used in the class or book you got this from? That is usually a good start.

 

[Jade_punk181]

Well I've seen the general theories ans tests but our teacher never gave us an example or a situation like this one, that is why I can't figure out how to even start the problem.

 

[Dick]

Try what VeeEight suggested. If s=7.54545454545 . . . what is 100*s-s?

 

[iRaid]

Yeah I posted that,but they deleted it and I got in trouble for giving them full answers so try doing something with s and SOMETHINGs and SUBTRACT them to get something S=something here. Then divide.