It should be noted however (as I do) that the decimal number is still not equivalent to the actual floating point number, only that when converted back it is th

It should be noted however (as I do) that the decimal number is still not equivalent to the actual floating point number, only that when converted back it is the same. Since 2 divides evenly into 10, every binary number has an exact decimal representation, and you can produce a decimal string which is equivalent to any floating point number. You may need quite a few digits, though.