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What is the smallest positive integer  n  such that n/2010 is a terminating decimal?

 Jun 14, 2019
 #1
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n = 201

201 / 2010 =0.1 = 1/10

 Jun 14, 2019
 #2
avatar+208 
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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

 Jun 15, 2019
 #3
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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, \(n = 3\cdot 67 = 201\).

 Jun 22, 2019

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