Decimal to IEEE 754 double precision (float64)
This is the number type used by JavaScript, Python and Excel, so here you can see why 0.1 + 0.2 is not exactly 0.3.
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Processing and privacy: The result is calculated inside your browser and your data is not sent to any server.
How to use it
- Enter decimal number.
- The result appears straight away and updates as you edit.
- Copy the result, or copy a link that keeps the same values to share it.
How it is calculated
Value = (-1)^S × 1.F × 2^(E - 1023), with a sign bit S, an 11-bit exponent E and a 52-bit fraction F. Rounded to the nearest representable value, ties to even.
Example
Inputs: Decimal number = 0.1. Result: Hex encoding: 0x3FB999999999999A; Value class: Normal.
0.1
0x3FB999999999999A
Limits and caveats
- Infinity, -Infinity and NaN are accepted; NaN uses the standard quiet pattern 0x7FF8000000000000.
- For very small numbers the stored value can run to hundreds of digits because it is written in full.
Questions about this tool
What is 0.1 as a double?
0x3FB999999999999A, storing 0.1000000000000000055511151231257827021181583404541015625.
Why is 0.1 + 0.2 not equal to 0.3?
All three are stored approximately, and the sum of the stored 0.1 and 0.2 lands on a different double from the stored 0.3.
What is the largest integer a double holds exactly?
2⁵³ = 9007199254740992. Beyond it not every integer fits, so 9007199254740993 becomes 9007199254740992.