In a base-3 number system, what is the product of '10' and '11'?

In a base-3 number system, what is the product of '10' and '11'?

Step 1: Understand that '10' in base-3 means 1*3^1 + 0*3^0, which equals 3 in decimal.
Step 2: Understand that '11' in base-3 means 1*3^1 + 1*3^0, which equals 4 in decimal.
Step 3: Multiply the decimal values: 3 (from '10') * 4 (from '11') = 12.
Step 4: Convert the decimal product (12) back to base-3. Start by finding the largest power of 3 less than or equal to 12.
Step 5: The largest power of 3 less than or equal to 12 is 9 (which is 3^2). 12 - 9 = 3.
Step 6: The next largest power of 3 is 3 (which is 3^1). 3 - 3 = 0.
Step 7: Since there are no remaining values, we have 1 for 3^2, 1 for 3^1, and 0 for 3^0.
Step 8: Write the base-3 representation: '110' (1 for 3^2, 1 for 3^1, and 0 for 3^0).

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