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 <em>x</em> be the number,
<em>x</em> = -1.353535...
Multiply <em>x</em> by 100 to move the decimal point two positions to the right:
100<em>x</em> = -135.353535...
Subtract <em>x</em> from 100<em>x</em> to eliminate the fractional part, then solve for <em>x</em> :
100<em>x</em> - <em>x</em> = -135.353535... - (-1.353535...)
99<em>x</em> = -135 + 1
99<em>x</em> = -134
<em>x</em> = -134/99
