My life is a lie!

I had a math issue, and while its not important, I thought it was kind of funny. Somehow it didn't quite do that math correctly. I typed ./r 577.2-172.8, and got 404.40000000000000000003.

0.2 = 2 * 1/10, 0.8 = 8 * 1/10. 1/10 is a repeating decimal in base-2, just like 1/3 is a repeating decimal in base-10. (In fact, any fraction whose denominator is not a power of 2 will have an infinite representation in base-2.) Computers are always working in base-2. If you round the binary representation of 0.1 to 24 bits, the result is the value 0.100000001490116119384765625. Floating-point arithmetic has problems, as well. For example (using 24-bit representations), 0.1 * 0.1 results in ~0.0100000003, whereas the representable number closest to 0.01 (the correct answer) is ~0.0099999998. For more fun, addition and multiplication remain commutative (a + b = b + a) in floating-point arithmetic, but they are not associative ((a + b) + c =/= a + (b + c)) or distributive ((a + b) * c =/= a * c + b * c). Floating-point precision errors have gotten people killed .

Thats actually really neat! (I mean not the dead people part) but the explanation. I did not know computers computed like that, it makes me wonder if financial institutions can benefit from little things like this when they are dealing with billions of dollars.

Money in computer systems is typically represented by integers, not floating point numbers. Hence no precision error. The bank makes money on stuff like investing capital for interest while it is being transfered and taking exorbiant fees for services that costs them nothing, but not through calculation errors.