To convert the decimal number 467 to base 9, we follow these steps:

1. Divide 467 by 9 and record the quotient and remainder. $467 \div 9 = 51 \text{ quotient}, \text{ remainder } 8$

2. Divide 51 by 9 and record the quotient and remainder. $51 \div 9 = 5 \text{ quotient}, \text{ remainder } 6$

3. Divide 5 by 9 and record the quotient and remainder. $5 \div 9 = 0 \text{ quotient}, \text{ remainder } 5$

Now, write the remainders from bottom to top:
$467_{10} = 568_9$

Thus, 467 in base 10 is equal to 568 in base 9.

Would you like more details on the conversion process?

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Here are 5 questions related to this topic:

1. How do you convert a number from base 9 back to base 10?
2. What is the importance of remainders in base conversions?
3. Can you convert 725 from base 10 to base 9?
4. What is the difference between base 9 and other commonly used bases like binary or hexadecimal?
5. How would you convert a decimal fraction to base 9?

Tip: To check if your base conversion is correct, you can convert the base 9 result back to base 10.