(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Convert 23.588 (the 88 is repeating) to an improper fraction.

2. Relevant equations

I don't have any.

3. The attempt at a solution

I'm not sure of the best way to go about this so I've taken a method that I've seen on some problems that were more simple as they didn't have the 23.5 in front of the repeating decimal.

I see that this can be broken down into:

23 + .5 + 8/10 + 8/10(1/10) + 8/10(1/10)^2...etc.

Although, I'm really not sure how to collapse the infinite progression of 8/10(1/10)^n into an actual number.

I've tried plugging 8/10 in for 'a' and 1/10 in for 'r' in the infinite progression equation:

a/(1-r)

This results in 8/9 then adding 1/2 to that we get 25/18 and then adding 23 to that I get 439/18

However, this result is not correct.

Any help/suggestions are welcome. Thank you for your time!

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# Homework Help: Convert repeating decimal to improper fraction

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