Final answer:
To express 533 base 6 as a number in base three, we need to convert it from base 6 to base 10 first, and then convert it from base 10 to base 3. The equivalent of 533 base 6 in base 3 is 211.
Step-by-step explanation:
To express 533 base 6 as a number in base three, we need to convert it from base 6 to base 10 first, and then convert it from base 10 to base 3. Here are the steps:
Step 1: Convert 533 base 6 to base 10. Using the positional notation, we can write it as:
5 × 62 + 3 × 61 + 3 × 60 = 180 + 18 + 3 = 201.
Step 2: Convert 201 base 10 to base 3. Divide the number by 3 repeatedly and record the remainders. The remainder of the last division is the least significant digit in base 3. The process is as follows:
201 ÷ 3 = 67 remainder 0.
67 ÷ 3 = 22 remainder 1.
22 ÷ 3 = 7 remainder 1.
7 ÷ 3 = 2 remainder 1.
2 ÷ 3 = 0 remainder 2.
So, the equivalent of 533 base 6 in base 3 is 211.