To convert the decimal number **64.005125** into binary, we handle the integer and fractional parts separately:

### Step 1: Convert the integer part (64) to binary
The integer part is 64. We'll repeatedly divide by 2 and note the remainders.

\[
64 \div 2 = 32 \text{ remainder } 0 \\
32 \div 2 = 16 \text{ remainder } 0 \\
16 \div 2 = 8 \text{ remainder } 0 \\
8 \div 2 = 4 \text{ remainder } 0 \\
4 \div 2 = 2 \text{ remainder } 0 \\
2 \div 2 = 1 \text{ remainder } 0 \\
1 \div 2 = 0 \text{ remainder } 1
\]

Reading the remainders from bottom to top, the binary representation of **64** is:

\[
64_{10} = 1000000_2
\]

### Step 2: Convert the fractional part (0.005125) to binary
For the fractional part, we multiply by 2 and keep track of the integer part. We stop when the fraction becomes zero or repeat after a reasonable number of steps.

1. \(0.005125 \times 2 = 0.01025\) (integer part = 0)
2. \(0.01025 \times 2 = 0.0205\) (integer part = 0)
3. \(0.0205 \times 2 = 0.041\) (integer part = 0)
4. \(0.041 \times 2 = 0.082\) (integer part = 0)
5. \(0.082 \times 2 = 0.164\) (integer part = 0)
6. \(0.164 \times 2 = 0.328\) (integer part = 0)
7. \(0.328 \times 2 = 0.656\) (integer part = 0)
8. \(0.656 \times 2 = 1.312\) (integer part = 1, fractional part = 0.312)
9. \(0.312 \times 2 = 0.624\) (integer part = 0)
10. \(0.624 \times 2 = 1.248\) (integer part = 1, fractional part = 0.248)
11. \(0.248 \times 2 = 0.496\) (integer part = 0)
12. \(0.496 \times 2 = 0.992\) (integer part = 0)
13. \(0.992 \times 2 = 1.984\) (integer part = 1, fractional part = 0.984)
14. \(0.984 \times 2 = 1.968\) (integer part = 1, fractional part = 0.968)

The binary for the fractional part goes: \(0.0000001011...\)

### Step 3: Combine the integer and fractional parts
Now, combine the binary parts:

\[
64.005125_{10} \approx 1000000.0000001011_2
\]

This binary representation is an approximation, as the fractional part continues infinitely.

Would you like to see more details or have any further questions?

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Here are five related questions you might want to explore:

1. How do you convert any decimal fraction to binary?
2. What are the advantages of using binary in computers?
3. How do you convert a binary fraction back to decimal?
4. How do you perform binary addition with fractional numbers?
5. How do floating-point numbers work in binary?

**Tip**: When converting fractions, be mindful that some decimal fractions cannot be exactly represented in binary.

Learn how to convert the decimal number 64.005125 to binary through a step-by-step process. Understand key concepts such as binary conversion for both integer and fractional parts, making this guide ideal for high school students in Grades 9-12.

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