How do I convert .009 to hex

Start by seeing how many times (1/16) divides into 0.009. The answer to that is less than 1, so the first digit of the hexadecimal number after the decimal point is 0. Then see how many times (1/16)^2 divides into 0.009; the answer to that is a bit more than 2, so the second digit is 2. Now subtract 2x (1/16)^2 from 0.009, leaving a remainder of 0.001188, and see how many times (1/16)^3 divides into that - the answer is 4. So at this point you have 0.024. Subtract 4x (1/16)^3 from 0.001188, leaving a remainder of 0.000211, divide that by (1/16)^4, etc, etc. Continue in this way until either (a) the remainder of one of the divisions is 0, so the decimal is terminated, (b) a repeating pattern emerges, or (c) you reach a level of accuracy sufficient for your purposes. In this case you should find that the hexadecimal version requires 15 hex digits to precisely equal 0.009 base 10.