Binary with decimal point → Decimal number

Enter a binary number like 101.011 or -0.00011. This tool computes the exact rational value (no rounding) and also shows what happens if you convert it to a JavaScript Number (IEEE-754 double), including the rounding error.

Exact value

As rational (numerator / denominator)

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As decimal

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JavaScript Number (IEEE-754 double) rounding

JS Number value

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|Exact − JS Number|

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Note: If the denominator is a power of 2 (it always is for finite binary fractions), the value is exactly representable in IEEE-754 as long as it fits in range; rounding mainly shows up when the magnitude is large or when you later print with limited digits.