Which term applies to numbers that cannot be written in this form a/b

Assuming 'a' and 'b' are integers, with b as nonzero, then a/b is known as a rational number. The term "ratio" is buried in "rational". A ratio is effectively a fraction of two values so that's a good way to remember the term. Some examples of rational numbers are 2/3 or 4/9. Whole numbers are rational because something like 7 is the same as 7/1

Any numbers that cannot be written as a ratio of whole numbers, we consider them irrational (aka opposite of rational, or not rational). Something like pi = 3.14 or sqrt(2) = 1.414 are irrational as we cannot express them in the form a/b. We can get close but not exact. 

In summary, the answer is irrational