To convert the decimal number \( 1386 \) to a binary number, we follow the division by 2 method:

1. Divide 1386 by 2:  
   \( 1386 \div 2 = 693 \) remainder \( 0 \)
2. Divide 693 by 2:  
   \( 693 \div 2 = 346 \) remainder \( 1 \)
3. Divide 346 by 2:  
   \( 346 \div 2 = 173 \) remainder \( 0 \)
4. Divide 173 by 2:  
   \( 173 \div 2 = 86 \) remainder \( 1 \)
5. Divide 86 by 2:  
   \( 86 \div 2 = 43 \) remainder \( 0 \)
6. Divide 43 by 2:  
   \( 43 \div 2 = 21 \) remainder \( 1 \)
7. Divide 21 by 2:  
   \( 21 \div 2 = 10 \) remainder \( 1 \)
8. Divide 10 by 2:  
   \( 10 \div 2 = 5 \) remainder \( 0 \)
9. Divide 5 by 2:  
   \( 5 \div 2 = 2 \) remainder \( 1 \)
10. Divide 2 by 2:  
    \( 2 \div 2 = 1 \) remainder \( 0 \)
11. Divide 1 by 2:  
    \( 1 \div 2 = 0 \) remainder \( 1 \)

Now, take the remainders from the last to the first:

So, \( 1386_{10} = 10101101010_2 \).

Would you like more details on binary conversions or have any questions?

Here are 5 related questions to expand on this concept:
1. How do you convert binary numbers back to decimal?
2. What is the binary equivalent of \( 543 \)?
3. How does binary addition work between two numbers?
4. What is the largest number you can represent with 8 bits in binary?
5. Can you explain how negative numbers are represented in binary using two's complement?

**Tip:** To quickly verify a binary conversion, convert it back to decimal by multiplying each bit by \(2^n\), where \(n\) is the bit's position from right to left, starting from 0.

Learn how to convert the decimal number 1386 to binary using the division by 2 method. This detailed step-by-step solution covers key concepts in number systems and binary conversions. Suitable for students in Grades 5-7.

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