Binary Fraction Converter

The rule

each place after the point is 1⁄2, 1⁄4, 1⁄8, …

Why 0.1 is not exact in binary

A fraction terminates in binary only when its denominator is a power of two. 0.375 is 3/8, so it is exactly 0.011. But 0.1 is 1/10, and 10 has a factor of 5 — so it recurs forever, exactly as 1/3 does in decimal.

That is the source of the classic floating-point surprise where 0.1 + 0.2 does not quite equal 0.3. Nothing is broken; the values simply cannot be stored exactly in binary.