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# Terminating Decimals

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What is the smallest positive integer $$\frac{n}{n+101}$$ such that  is equal to a terminating decimal?

Thanks!

Aug 5, 2019

#1
+6203
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In order for a fraction to have a terminating decimal representation the denominator must

have factors of only powers of 2 or 5.

when n=24, n+101=125 which is 53

This appears to be the smallest positive integer meeting the criterion.

Aug 5, 2019
#2
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Thanks rom :)

Aug 6, 2019