Add.
1122 Subscript three
plus 2020 Subscript three


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.

Add 1122 Subscript three plus 2020 Subscript three

Learn how to add numbers in base 3 with this example: 1122_3 + 2020_3. This guide includes step-by-step base 3 to base 10 conversion, addition, and converting the result back to base 3. Suitable for Grades 7-9 students exploring number systems and base conversions.

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