### Instruction: Convert $\frac{3}{16}$ to base 2. Express your answer in binary with a radix point.### Response: To convert a fraction to base 2, I need to multiply it by 2 repeatedly and record the integer parts as the digits after the radix point.
For example, $\frac{3}{16} \times 2 = \frac{6}{16} = \frac{3}{8}$, so the first digit after the radix point is 0.
Then, $\frac{3}{8} \times 2 = \frac{6}{8} = \frac{3}{4}$, so the second digit is 0 as well.
Next, $\frac{3}{4} \times 2 = \frac{6}{4} = 1 + \frac{2}{4}$, so the third digit is 1 and I have a remainder of $\frac{1}{2}$.
Continuing, $\frac{1}{2} \times 2 = 1$, so the fourth digit is 1 and I have no remainder left.
This means I can stop multiplying by 2 and write the final answer as a binary fraction.