To convert the decimal number 610 to a binary number, follow these steps:

1. Divide the number by 2 and write down the quotient and remainder.
2. Continue dividing the quotient by 2 until the quotient becomes 0, noting each remainder.
3. The binary representation is obtained by reading the remainders in reverse order (from bottom to top).

Let's go through the steps:

\[
610 \div 2 = 305 \text{ remainder } 0
\]
\[
305 \div 2 = 152 \text{ remainder } 1
\]
\[
152 \div 2 = 76 \text{ remainder } 0
\]
\[
76 \div 2 = 38 \text{ remainder } 0
\]
\[
38 \div 2 = 19 \text{ remainder } 0
\]
\[
19 \div 2 = 9 \text{ remainder } 1
\]
\[
9 \div 2 = 4 \text{ remainder } 1
\]
\[
4 \div 2 = 2 \text{ remainder } 0
\]
\[
2 \div 2 = 1 \text{ remainder } 0
\]
\[
1 \div 2 = 0 \text{ remainder } 1
\]

Reading the remainders from bottom to top, we get:

\[
610_{10} = 1001100010_2
\]

Thus, the binary representation of 610 is **1001100010**.

Would you like further details or have any questions?

Here are 5 related questions for practice:
1. Convert 256 to binary.
2. What is the binary representation of 1023?
3. How do you convert a binary number back to decimal?
4. What is the binary representation of 45?
5. How do you perform binary addition?

**Tip:** Binary numbers are the foundation of computer processing, representing data using just 0s and 1s!

Learn how to convert the decimal number 610 into binary using the division-by-2 method. This solution walks through each step with remainders and explains how to read the binary digits in reverse order. Perfect for students in Grades 5-7 learning about number systems.

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