+4622 What is the smallest positive integer n such \(n/2010\) that is a terminating decimal?
+129847 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
2010 = 2 * 3 * 5 * 67
3 x 67 =201- The smallest positive integer, because:
201/2010 =0.1
+129847 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
