To convert the decimal number $0.65625$ to binary, follow these steps:

1. Convert the fractional part to binary:

   • Multiply the fractional part by 2. Write down the integer part (0 or 1) and continue with the fractional part.

   $0.65625 \times 2 = 1.3125 \quad (\text{Integer part = 1})$ $0.3125 \times 2 = 0.625 \quad (\text{Integer part = 0})$ $0.625 \times 2 = 1.25 \quad (\text{Integer part = 1})$ $0.25 \times 2 = 0.5 \quad (\text{Integer part = 0})$ $0.5 \times 2 = 1.0 \quad (\text{Integer part = 1})$

   • The process stops when the fractional part becomes 0.

2. Combine the integer parts:

   • The binary equivalent is obtained by combining the integer parts from each step: $0.65625_{10} = 0.10101_2$

So, the decimal number $0.65625$ in binary is $0.10101_2$.

Would you like more details or have any questions?

Related Questions:

1. How do you convert $0.25$ to binary?
2. What is the binary representation of $0.75$?
3. How do you convert a binary fraction back to decimal?
4. What is the general method for converting any fractional decimal to binary?
5. Can you convert $0.33333$ (repeating) to binary?
6. What is the difference between converting repeating and terminating decimals to binary?
7. How precise can binary fractions be compared to decimal fractions?
8. How do you represent binary fractions in floating-point notation?

Tip:

For binary conversion of fractions, each multiplication by 2 moves the decimal point one place to the left in binary, helping to identify the binary digits sequentially.