How Do You Convert Base 10 Fractions In To Binary Decimals?

To convert integers from base 10 (decimal) representation to base 2 (binary) representation, one must break up the number into pieces that are powers of 2. Similar processes can be used to convert non-integers into binary form. This article will show 3 (or 11, in binary) methods of converting fractions into binary decimals.

*Method 1* To convert a fraction, first convert the numerator and denominator into binary, and then apply binary long division. This is the normal method for converting fractions into base 10 decimals. For example, let´s use this technique to convert 13/22.

First, 13/22 becomes 1101/10110 in base 2. Then, 1101 divided by 10110 is 0.1001011101000..., with repetition of the digit sequence 1011101000. This can be cumbersome if you don't like doing long division in base 2, so you may want to try the next method.

*Method 10* Break up the fraction into powers of 1/2, and then use the following list to build the binary decimal: 1/2 = 0.1 1/4 = 0.01 1/8 = 0.001 1/16 = 0. ... more.

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