



 
Hi Emma, I am going to try to explain using the repeating decimal 0.15151515... Write 0.15151515... as
This is the geometric series
with a = 15/100 and r = 1/100. I don't know if you have seen geometric series in your algebra classes yet but if you haven't you will see them soon. In a response to a previous question Claude and I showed that if r < 1 then the series
approaches a/(1  r) as the number of terms approaches infinity. In the case of 0.15151515.. this means that
A similar argument works for all the examples you sent. Penny  


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