To convert the decimal number $0.65625$ to a binary number, we need to handle the fractional part of the decimal separately from the integer part.

Step-by-Step Conversion:

1. Start with the decimal fraction: $0.65625$.

Multiply the fractional part by 2 and note the integer part after each step. Keep multiplying the fractional part of the result until it becomes zero or repeats.

$0.65625 \times 2 = 1.3125 \quad \text{(integer part is 1)}$ $0.3125 \times 2 = 0.625 \quad \text{(integer part is 0)}$ $0.625 \times 2 = 1.25 \quad \text{(integer part is 1)}$ $0.25 \times 2 = 0.5 \quad \text{(integer part is 0)}$ $0.5 \times 2 = 1.0 \quad \text{(integer part is 1, fractional part becomes zero)}$

Now, collect all the integer parts: $1, 0, 1, 0, 1$.

Thus, the binary representation of $0.65625$ is: $0.65625_{10} = 0.10101_2$

Would you like more details on the process?

Related Questions:

1. How do you convert a binary fraction back to decimal?
2. What is the process to convert any decimal number to a binary fraction?
3. How would you convert $0.8125$ to binary?
4. What is the binary representation of $0.375$?
5. How do you add two binary fractions?

Tip: When converting decimal fractions to binary, the conversion process can result in repeating binary digits if the fraction cannot be exactly represented.