In a base 3 system, what is the representation of the decimal number 5? (2023)

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Q: In a base 3 system, what is the representation of the decimal number 5? (2023)

Solution: In base 3, the decimal number 5 is represented as '12' (1*3^1 + 2*3^0 = 3 + 2 = 5).

Steps: 8

Step 1: Understand that we need to convert the decimal number 5 into base 3.
Step 2: Identify the largest power of 3 that is less than or equal to 5. The powers of 3 are 1 (3^0 = 1), 3 (3^1 = 3), and 9 (3^2 = 9). The largest power of 3 less than 5 is 3 (3^1).
Step 3: Determine how many times 3 (3^1) fits into 5. It fits 1 time, so we write down '1' for the 3's place.
Step 4: Subtract 3 from 5. This gives us 5 - 3 = 2.
Step 5: Now, we need to represent the remaining 2 in base 3. The largest power of 3 that fits into 2 is 1 (3^0 = 1).
Step 6: Determine how many times 1 (3^0) fits into 2. It fits 2 times, so we write down '2' for the 1's place.
Step 7: Combine the digits we found. The digit for 3's place is 1 and for 1's place is 2, so we write '12'.
Step 8: Therefore, the representation of the decimal number 5 in base 3 is '12'.