+0

Anotherone!

+5
197
3
+2765

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

tertre  Mar 14, 2017

#2
+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

CPhill  Mar 14, 2017
#1
+5

2010 = 2 * 3 * 5 * 67

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

201/2010 =0.1

Guest Mar 14, 2017
#2
+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

CPhill  Mar 14, 2017
#3
+2765
+5

It is! Thanks!

tertre  Mar 14, 2017
{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}