SP#6: Unit K Concept 10: Repeating decimal as a rational number

First, write the decimals in a pattern, like the one that I did below the original problem. Ignore the 2 until the end. We get our "a" sub "1" by the first decimal which is 96/100, and our ratio is 1/100. Using summation notation and the geometric infinite formula we can start plugging in. The summation notation will also use the geometric sequence formula and you already have the ratio and the"a" sub "1". Next will be the infinite geometric series and just plug in (96/100) / 1-(1/100). You subtract the 1 to 1/100 and get 99/100. With (96/100) / (99/100), use the reciprocal of 99/100 and multiply it to the numerator and denominator. Now you should have 96/99, and this is were you include the 2 from the beginning. Add 2 to 96/99 and your answer will be 294/99 but reduced will be 98/33.

Well in my opinion for this problem your need to pay attention to the reciprocal part. It can be confusing and it's easy to make a mistake here. Also the part when you add 2 to 96/99 because you have to reduce and it can get tricky if you do it wrong.