It is considered rational since it can be defined as p/q with both p and q being integers.

In short it is a ratio of two numbers thus rational.
But i Think It Irrational because Its Non-Terminating
non terminating decimals can be rational as long as it can be expressed as a fraction
4/37 is repeating decimal. all repeating decimals can be expressed in fraction, therefore, rational. Pi (3.1416.....) is non-terminating, therefore, irrational.
So, answer above is right. 4/37 is rational.
 Always remember that a rational number can be expressed as a quotient. :)
It's obvious that the fraction "4/37" is expressed as quotient (based on your definition of rational number"). A fraction is a ratio of two numbers, p/q where q is not equal to zero. Therefore, 4/37 is a rational number.