Converting fractional portion of a number to binary.
  Assume 8 bits of data storage.




Decimal.Decimal to binary

 .431

 .431 c .
0.862 c 0
1.724 c 1
1.448 c 1
0.896 c 0
1.792 c 1
1.584 c 1
1.168 c 1
0.336 c 0

.01101110b


   


Binary to Decimal.Decimal

0.01101110

sum=            0 
0 *        .5 + 0
1 *       .25 + 0
1 *      .125 + 0.25
0 *     .0625 + 0.375
1 *    .03125 + 0.40625
1 *   .015625 + 0.421875
1 *  .0078125 + 0.4296875
0 * .00390625 + 0.4296875

sum=            0.4296875



Note the difference between values 

0.431 - 0.4296875 = .0013125   (.3% difference)