So this concept is to show you how to write a repeating decimal as a rational number using geometric series. Well, basically you identify where the numbers are repeating and of corse this is infinite. So in my problem the number that repeats is 29 and the problem is .29292929 so the series will start .29+.0029+.000029+.00000029,..... We do this to find the "r" which in this case is .01. Then once we have a one and the r its possible to plug it in to the geometric series sum formula. So the sum formula for infinite series is a one over 1-r, or a one/1-r. then after we pug it in we will have 29/100 and 99/100 on the bottom. So we then switch them since you are dividing fractions the 100s cancel out and you are left with 29/99. Which can't be simplified so its your answer.
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