To convert the decimal number $143$ to base $12$, we need to repeatedly divide the number by $12$ and keep track of the remainders.

Step-by-Step Conversion

1. Divide 143 by 12: $143 \div 12 = 11 \quad \text{remainder } 11$ So, the remainder is $11$, and the quotient is $11$.

2. Divide the quotient (11) by 12: $11 \div 12 = 0 \quad \text{remainder } 11$ The remainder is $11$, and the quotient is $0$.

3. Collect the remainders from bottom to top: The remainders are $11$ and $11$. In base $12$, the digits from $0$ to $9$ are represented normally, and $10$ is represented by the letter "A" and $11$ by the letter "B".

   Therefore, $11$ in base $12$ is "B".

Final Result

Combining the remainders, the number $143$ in base $12$ is:

$143_{10} = BB_{12}$

Would you like more details or have any questions about this conversion?

Related Questions:

1. How do you convert numbers from base $12$ back to decimal?
2. What are other methods for converting numbers between different bases?
3. How would you convert a fractional decimal number to base $12$?
4. What is the significance of different number bases in mathematics?
5. How do number bases apply in computer science, such as base $2$ (binary)?

Tip: When converting numbers to other bases, start with the largest base power that fits into the number to simplify the process!