Which one of the following is a non-terminating and repeating decimal? 

Concept used:

Non-terminating: A decimal number that continues endlessly, with no group of digits repeating endlessly.

Repeating decimal:  A number whose decimal representation eventually becomes periodic (i.e. the same sequence of digits repeats indefinitely).

Calculation:

According to the above options,

⇒ \(\frac{13}{8}\) = 1.625

⇒ \(\frac{3}{16}\) = 0.1875

⇒ \(\frac{3}{11}\) = 0.272727

⇒ \(\frac{137}{25}\) = 5.48

∴ The required non-terminating and repeating decimal is \(\frac{3}{11}\).