Javascript Round error

Question

I have a problem with rounding numbers.

x = 0.175;
console.log(x.toFixed(2));
// RESULT: 0.17

x = 1.175;
console.log(x.toFixed(2));
// RESULT: 1.18

x = 2.175;
console.log(x.toFixed(2));
// RESULT: 2.17

Why is (X!=1).175 not rounded to X.18?

Answer 1

The problem here is that 0.175 is a repeating decimal in binary (specifically, after a short prefix, it settles down to a repeating 0011 pattern). When represented in a finite floating point representation, this repeating pattern gets truncated. When you change the integer part from 0 to 1 to 2, you are adding one additional bit each time to the integer part of the number, which pushes off one trailing bit. Depending on what bit value gets pushed off, that can change the rounded value enough to affect the visible result. Note that after 2.175, the next change in rounding behavior doesn't occur until 8.175 (after two more low-order bits have been pushed off the representation).