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March 10th, 2014, 11:26 PM   #1
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Repeating decimal problem

A pollster found that 36.72(3672)% of her sample voted Republican. What is the smallest number of people that could have been in the sample?
NOTE: The parenthesis number (3672) is a repeating decimal and I will use this notation throughout this problem

36.72(3762)% = 0.(3672)
Let x = 0.(3672)
10000x = 3672.(3672)
9999x = 3672
x = 3672/9999 = 408/1111...this is in simplest form
So the smallest number of people that could have been in the sample is 1,111

Am I correct. Is there another way to solve this problem? Thanks
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March 12th, 2014, 08:46 AM   #2
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That's completely correct, except that you mistyped 3672 as 3762 at one point. You used the best method. If you did other problems of a similar nature, you would know how to just write down the relevant fraction, but using a little algebra to explain it is okay. If you're not allowed to use a calculator for this problem, a fussy teacher might expect you to state why 408/1111 is the simplest form.
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