Question

-1.3535353 is it a rational

Answer 1

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