What is the smallest positive integer n such that n/2010 is a terminating decimal?
n = 201
201 / 2010 =0.1 = 1/10
I would do it a different way:
2010 prime factor=201 and 2 and 5
2 and 5 don't make a decimal so 201.
201/2010=1/10=0.1
Hope this helps... :P
Theorem: If the denominator of a simplest fraction is 2a 5b, then the fraction is terminating.
2010 = 2 * 3 * 5 * 67
We need to eliminate 3 and 67 from the denominator.
Therefore, \(n = 3\cdot 67 = 201\).
+586 
