Series & Sequences: Express 7.54545454545 as Rational Number

In summary, the problem is to express 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 suggested method is to multiply the number by 100 and subtract it from itself, then use division to find p/q. However, the person asking for help has not seen this method before and is unsure how to start the problem. Another suggestion is to use the variable s to represent the repeating decimal and subtract it from itself in a similar way.
  • #1
Jade_punk181
3
0

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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  • #2
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.
 
  • #3
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.
 
  • #4
Try what VeeEight suggested. If s=7.54545454545 . . . what is 100*s-s?
 
  • #5
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.
 

FAQ: Series & Sequences: Express 7.54545454545 as Rational Number

What is a series and sequence?

A series is a sum of terms in a particular order, while a sequence is a list of numbers following a specific pattern.

How do you express a repeating decimal as a rational number?

To express a repeating decimal as a rational number, you can create an equation where the repeating decimal is equal to a variable, and then solve for that variable using algebra.

Can all repeating decimals be expressed as rational numbers?

Yes, all repeating decimals can be expressed as rational numbers, as long as they are truly repeating and not just a finite number of decimals that happen to repeat.

What is the process for converting a repeating decimal to a rational number?

The process for converting a repeating decimal to a rational number is to identify the pattern of repetition, set it equal to a variable, and solve for the variable using algebra. Then, the resulting fraction will be the rational number equivalent of the repeating decimal.

Why is it important to understand series and sequences?

Understanding series and sequences is important in various fields of science, such as physics and biology, as they help in predicting and analyzing patterns and trends. They also play a crucial role in mathematical calculations and problem solving.

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