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+5
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avatar+2765 

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

tertre  Mar 14, 2017

Best Answer 

 #2
avatar+87301 
+5

I believe that this is correct.....

 

2010 factors as   2 * 3 * 5 * 67

 

And a fraction will be a terminating decimal whenever its denominator can only be written in terms of 2 or 5   (or both)

 

So

 

(3 * 67)  / (2 * 3 * 5 * 67)  =  1/ [2 * 5 ]  =   1/10

 

So...the smallest integer  is 3* 67   =  201

 

 

cool cool cool

CPhill  Mar 14, 2017
 #1
avatar
+5

2010 = 2 * 3 * 5 * 67

 

3 x 67 =201- The smallest positive integer, because:

201/2010 =0.1

Guest Mar 14, 2017
 #2
avatar+87301 
+5
Best Answer

I believe that this is correct.....

 

2010 factors as   2 * 3 * 5 * 67

 

And a fraction will be a terminating decimal whenever its denominator can only be written in terms of 2 or 5   (or both)

 

So

 

(3 * 67)  / (2 * 3 * 5 * 67)  =  1/ [2 * 5 ]  =   1/10

 

So...the smallest integer  is 3* 67   =  201

 

 

cool cool cool

CPhill  Mar 14, 2017
 #3
avatar+2765 
+5

It is! Thanks! 

tertre  Mar 14, 2017

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