+0

Number Theory Help

+1
157
3
+544

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

Jun 14, 2019

#1
0

n = 201

201 / 2010 =0.1 = 1/10

Jun 14, 2019
#2
+208
-4

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
+7725
0

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