To add the numbers \( 2101_3 \) and \( 102_3 \) in base 3, we can follow these steps:

1. **Align the numbers** for addition:
   ```
      2101
   +   0102
   ```

2. **Add column by column** from right to left:
   - **First column** (rightmost): \( 1_3 + 2_3 = 3_3 \). Since 3 in base 3 is represented as \( 10_3 \), we write down 0 and carry over 1.
   - **Second column**: \( 0_3 + 0_3 + 1_3 \text{ (carried over)} = 1_3 \). No carry.
   - **Third column**: \( 1_3 + 1_3 = 2_3 \). No carry.
   - **Fourth column** (leftmost): \( 2_3 + 0_3 = 2_3 \). No carry.

3. **Write the result** down as follows:
   ```
      2200_3
   ```

Thus, the sum of \( 2101_3 \) and \( 102_3 \) in base 3 is \( 2200_3 \).

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Do you want more details or have any questions? 

Here are some related questions:

1. How do you convert base 3 numbers to base 10?
2. What is the base 10 equivalent of \( 2200_3 \)?
3. How do you subtract numbers in base 3?
4. Can you multiply numbers in base 3 directly without converting to base 10?
5. What is the general method to convert any base-n number to another base-m number?
6. How do you represent the number 10 (decimal) in base 3?
7. What are the rules for carrying over digits in different bases?
8. Can you provide an example of division in base 3?

**Tip:** When adding numbers in non-decimal bases, be careful to apply the correct base-specific rules for carrying over digits.

Explore how to add numbers in base 3 with a step-by-step explanation. This page covers the addition process for numbers 2101 base 3 and 102 base 3, including alignment, column-wise addition, and carrying over in base 3. Ideal for students learning about number systems and base conversions.

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