In this student problem, I had to write a decimal as a rational number using geometric series.
1)Find the term that is being repeated in the decimal
2)Depending on the length of the term(1,2,3), the next term should have an added 0 for every term that is repeated. So, if your repeated term is .34, your next term would be .0034. For this problem, my repeated factor was 687 so my next factors only had to continuously add 3 zeros.
3)You then divide the 2nd term by the previous term in order to find your ratio. My ratio was 1/1000 in this case.
4)Plug in the variables into the summation notation
5)Plug your variables into the formula, a sub 1 times 1-r^n divided by 1-r
6)In order to solve from there, I multiplied the top and bottom by 1000/999 so cancel out the denominators. I was left with 687/999 as my final answer
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