Floating point representations seem to do integer arithmetic correctly - why?

Question

I\'ve been playing around with floating point numbers a little bit, and based on what I\'ve learned about them in the past, the fact that 0.1 + 0.2 ends up bein

Answer 1

I'm writing that under assumption that Javascript uses double-precision floating-point representation for all numbers.

Some numbers have an exact representation in the floating-point format, in particular, all integers such that |x| < 2^53. Some numbers don't, in particular, fractions such as 0.1 or 0.2 which become infinite fractions in binary representation.

If all operands and the result of an operation have an exact representation, then it would be safe to compare the result using ==.

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What number in binary can only be represented as an approximation?

Why can't decimal numbers be represented exactly in binary?