Let's add the numbers $1122_3$ and $2020_3$, where the subscript 3 indicates they are in base 3.

Step 1: Convert the numbers to base 10.

1. Convert $1122_3$ to base 10:

$1122_3 = 1 \cdot 3^3 + 1 \cdot 3^2 + 2 \cdot 3^1 + 2 \cdot 3^0$

$1122_3 = 1 \cdot 27 + 1 \cdot 9 + 2 \cdot 3 + 2 \cdot 1 = 27 + 9 + 6 + 2 = 44$

2. Convert $2020_3$ to base 10:

$2020_3 = 2 \cdot 3^3 + 0 \cdot 3^2 + 2 \cdot 3^1 + 0 \cdot 3^0$

$2020_3 = 2 \cdot 27 + 0 \cdot 9 + 2 \cdot 3 + 0 \cdot 1 = 54 + 0 + 6 + 0 = 60$

Step 2: Add the base 10 equivalents.

$44 + 60 = 104$

Step 3: Convert the sum back to base 3.

To convert $104$ to base 3, we divide by 3 and record the remainders:

$104 \div 3 = 34 \ \text{remainder} \ 2$ $34 \div 3 = 11 \ \text{remainder} \ 1$ $11 \div 3 = 3 \ \text{remainder} \ 2$ $3 \div 3 = 1 \ \text{remainder} \ 0$ $1 \div 3 = 0 \ \text{remainder} \ 1$

Now, read the remainders from bottom to top: $104_{10} = 10212_3$.

Final Answer:

$1122_3 + 2020_3 = 10212_3$

Would you like more details or have any questions?

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Here are some related questions:

1. How do you convert a decimal number to base 3?
2. What are other examples of base conversions between base 3 and base 10?
3. How does carrying work when adding numbers in base 3?
4. How would you subtract $1122_3$ from $2020_3$?
5. Can you explain multiplication in base 3?

Tip: When converting between bases, working through each step carefully helps ensure you avoid mistakes, especially with remainders.