Series & Sequences: Express 7.54545454545 as Rational Number

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Homework Help Overview

The problem involves expressing the repeating decimal 7.54545454545 as a rational number in the form p/q, where p and q are positive integers with no common factors. The original poster expresses uncertainty about how to approach this problem, indicating it is unlike anything they have encountered before.

Discussion Character

  • Exploratory, Assumption checking

Approaches and Questions Raised

  • Some participants mention a common method involving multiplication and subtraction to isolate the repeating part of the decimal. Others inquire about the methods learned in class or from textbooks, suggesting a lack of direct examples provided by the teacher.

Discussion Status

Participants are exploring various approaches to the problem, with some suggesting specific algebraic manipulations. There is a recognition of the need for a structured method, but no consensus on a definitive approach has been reached yet.

Contextual Notes

There is mention of classroom constraints, such as the absence of examples from the teacher, which may be contributing to the participants' difficulties in starting the problem.

Jade_punk181
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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.
 
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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.
 
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.
 
Try what VeeEight suggested. If s=7.54545454545 . . . what is 100*s-s?
 
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.
 

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