Which of the following rational numbers has a non-terminating decimal expansion? 

It is known that a rational number$\frac{p}{q}$, where p and q are co-prime, has a terminating decimal expansion, if q can be prime factorised in the form of 2ⁿ5^m, where n and m are non-negative integers. 

Now, 

$\frac{17}{100}=\frac{17}{2\times 2\times 5\times 5}=\frac{17}{2^2\times 5^2}$ 

$\frac{11}{392}$, 11 and 392 are co-prime 

$\frac{13}{20}=\frac{13}{2\times 2\times 5}=\frac{13}{2^2\times 5}$ 

$\frac{19}{500}=\frac{19}{2\times 2\times 5\times 5\times 5}=\frac{19}{2^2\times 5^3}$ 

Here, except the rational number $\frac{11}{392}$, the denominator of every other rational number is of the form 2ⁿ5^m, where n and m are non-negative integers. 

∴$\frac{11}{392}$ has a non-terminating decimal expansion.