Binary Numeral System - Fractions in Binary

Fractions in Binary

Fractions in binary only terminate if the denominator has 2 as the only prime factor. As a result, 1/10 does not have a finite binary representation, and this causes 10 × 0.1 not to be precisely equal to 1 in floating point arithmetic. As an example, to interpret the binary expression for 1/3 = .010101..., this means: 1/3 = 0 × 2−1 + 1 × 2−2 + 0 × 2−3 + 1 × 2−4 + ... = 0.3125 + ... An exact value cannot be found with a sum of a finite number of inverse powers of two, and zeros and ones alternate forever.