MathRevolution wrote:

If r, s are positive integers, is r/s a terminating decimal?

1) 1/r is a terminating decimal

2) 1/s is a terminating decimal

* A solution will be posted in two days.

Decimal is terminating when it can be expressed as \(\frac{K}{2^n5^m}\), where n, m are non-negative integers and k is an integer (e. g. 0.1 can be expressed as \(\frac{1}{2^15^1}\); 0.015 can be expressed as \(\frac{15}{2^35^3}\) or \(\frac{3}{2^35^2}\) etc)

1) \(\frac{1}{r}\) is a terminating decimal, thus, can be expressed as \(\frac{1}{2^n5^m}\), \(r=2^n5^m\).

If s=5, then \(\frac{r}{s}=\frac{2^n5^m}{5}\), terminating.

If s=3, then \(\frac{r}{s}=\frac{2^n5^m}{3}\), not terminating.

Insufficient.

2) \(s=2^n5^m\)

\(\frac{r}{s}=\frac{r}{2^n5^m}\). Since r, s are positive integers, then the expression is a terminating decimal for any r,s.

Sufficient.

B