Repeating decimals are fun! Every repeating decimal is the sum of an infinite geometric series. The key to finding the answer is to write the decimal all as a quotient of integers. In other words, as a fraction. An example would be...
Given: 0.232323...
First step: write as a geometric series
0.23 + 0.0023 + 0.000023 + 0.00000023 + ...
Second step: find the sum
23/100 + 23/10,000 + 23/1,000,000 + ...
r(the pattern) = 1/100
Use the formula S = a/1-r
S = (23/100)/(1-(1/100)) = (23/100)/(99/100) = 23/99
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