To convert the decimal number **513** to octal, follow these steps:

1. Divide 513 by 8 and record the quotient and remainder:
   \[
   513 \div 8 = 64 \text{ remainder } 1
   \]

2. Divide the quotient (64) by 8:
   \[
   64 \div 8 = 8 \text{ remainder } 0
   \]

3. Divide the quotient (8) by 8:
   \[
   8 \div 8 = 1 \text{ remainder } 0
   \]

4. Finally, divide the quotient (1) by 8:
   \[
   1 \div 8 = 0 \text{ remainder } 1
   \]

Now, read the remainders from bottom to top: **1001**.

Thus, **513** in decimal is **1001** in octal.

Would you like more details on this conversion, or do you have any questions?

Here are 5 related questions:
1. How do you convert octal numbers to decimal?
2. How do you convert decimal numbers to binary?
3. How do you convert a binary number to octal?
4. What is the relationship between binary, octal, and hexadecimal systems?
5. How can I perform octal addition and subtraction?

**Tip:** When converting between number systems, grouping bits or digits (like in binary to octal) can simplify the process.

Learn how to convert the decimal number 513 to its octal equivalent using step-by-step base conversion methods. This guide explains the division-by-8 technique, making it easy for students to understand number system conversions. Perfect for Grades 6-8.

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