I hesitate because I'm not sure what you mean by "give the short form". I think you mean the period to be the interval at which the decimal repeats and the length of that repetition.

(a) 1.666...period = 6, length = 1

(b) -1.666...period = 6, length = 1

(c) 0.457...period = 457, length = 3

(d) 5.3624...period = 3264, length = 4

(e) -1.0413...period = 13, length = 2

(f) 15.0122...period = 122, length = 3

A rational number is any number that can be represented as a fraction in which the numerator and denominators are integers, and the denominator is not equal to zero.

Did this, at all, answer your questions?