Fraction Decimal to Binary Converter
Enter an exact fraction to convert its whole and fractional parts to binary. Repeated remainders are detected and shown with parentheses around the repeating bits.
Written and checked by TheToolNet Editorial Team · Last reviewed: September 20, 2026 · Editorial method
Convert a fraction to binary
Fractional decimal to binary method
Convert the whole-number part by ordinary base-two division. For the fractional remainder, multiply by 2. The whole part of each product becomes the next binary digit; carry the new fractional remainder into the next step.
For 1/2, the first multiplication gives one whole bit and no remainder, so the result is 0.1₂. For 1/10, the remainders repeat, producing 0.0(0011)₂.
When does a binary fraction terminate?
After reducing the fraction, a base-two expansion terminates only when the denominator is a power of 2. Denominators containing any other prime factor produce a repeating expansion.
| Fraction | Binary | Status |
|---|---|---|
| 1/2 | 0.1 | Terminates |
| 3/8 | 0.011 | Terminates |
| 1/3 | 0.(01) | Repeats |
| 1/10 | 0.0(0011) | Repeats |
Frequently asked questions
What do parentheses mean in binary?
The bits inside repeat forever. This is the base-two counterpart of a recurring decimal.
Does the converter round?
No. It detects an exact terminating result or repeating cycle using integer remainders.
Can I convert a binary integer?
Use the binary-to-decimal guide or binary-to-hexadecimal converter.