Decimal Fraction to Binary

Decimal fraction to binary: method

A decimal fraction can be written in binary by repeatedly multiplying the fractional part by 2.

1. Multiply by 2. Keep only the fractional part for the next step.
2. Record the integer part each time: it will be either 0 or 1.
3. Continue until the fraction becomes 0 or until the pattern clearly repeats.
4. Read the bits in order from top to bottom to form the binary fraction.

Example of the process

If the fraction is not already simple, work step by step:

• multiply the fraction by 2,
• note whether the result is below 1 or at least 1,
• use that digit as the next binary digit after the point.

Simplify the final answer

If the binary fraction has trailing zeros, they do not change the value and can usually be removed. Write the answer in its shortest correct form.

Check your work

Convert the binary fraction back to base 10 by adding the place values after the binary point. If you recover the original decimal fraction, your answer is correct.