Convert the decimal number 0.65625 to binary number

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.

Learn the step-by-step process to convert the decimal number 0.65625 to its binary equivalent. This guide covers essential concepts like fractional binary conversion and provides a detailed explanation suitable for students in Grades 6-8.

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