To convert 3183 from base 10 (decimal) to base 5, we follow these steps:

1. Divide the number by 5, keeping track of the quotient and remainder.
2. Continue dividing the quotient by 5 until the quotient becomes zero.
3. The base 5 numeral will be the remainders read in reverse order.

Let's begin:

$3183 \div 5 = 636 \text{ remainder } 3$ $636 \div 5 = 127 \text{ remainder } 1$ $127 \div 5 = 25 \text{ remainder } 2$ $25 \div 5 = 5 \text{ remainder } 0$ $5 \div 5 = 1 \text{ remainder } 0$ $1 \div 5 = 0 \text{ remainder } 1$

Reading the remainders from bottom to top, we get: $1 0 0 2 1 3_5$.

Thus, the base 5 representation of 3183 is 100213.

Would you like further details or explanations?

Here are 5 related questions for practice:

1. Convert 512 from base 10 to base 5.
2. How would you convert a base 5 number back to base 10?
3. What is the base 7 equivalent of the decimal number 3183?
4. How can you quickly check if a base conversion was done correctly?
5. What is the largest number that can be represented with three digits in base 5?

Tip: When converting from base 10 to any other base, always remember to read the remainders from bottom to top for the correct result.