Yes, it's rational.
If the digits after the decimal point terminate, then the number is
-1.3535353 = - 13,535,353/10,000,000
If they don't stop, then let x be the number,
x = -1.353535...
Multiply x by 100 to move the decimal point two positions to the right:
100x = -135.353535...
Subtract x from 100x to eliminate the fractional part, then solve for x :
100x - x = -135.353535... - (-1.353535...)
99x = -135 + 1
99x = -134
x = -134/99
