This is never obvious until you encounter it, but computers represent floating-point numbers in an interesting way. perlfaq4's "Why am I getting long decimals (eg, 19.9499999999999) instead of the numbers I should be getting (eg, 19.95)?" says:

Internally, your computer represents floating-point numbers in binary. Digital (as in powers of two) computers cannot store all numbers exactly. Some real numbers lose precision in the process. This is a problem with how computers store numbers and affects all computer languages, not just Perl.

It also points to the PDF What Every Computer Scientist Should Know About Floating-Point Arithmetic.

One of the easiest solutions is to store monetary values as pennies (or whatever the fractional amount of your local currency is) to avoid floating point values altogether.

(As a side note, if you're declaring numeric values, you're better off writing my $first_num = -3500.78; without the quotes; there's no need to make them string values if you're going to treat them as numerics.)