In a base 3 system, what is the equivalent of the decimal number 5?

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Question: In a base 3 system, what is the equivalent of the decimal number 5?

Options:

Correct Answer: 21

Solution:

The decimal number 5 is represented as 12 in base 3 (1*3^1 + 2*3^0 = 3 + 2 = 5).

In a base 3 system, what is the equivalent of the decimal number 5?

In a base 3 system, what is the equivalent of the decimal number 5?

Step 1: Understand that we need to convert the decimal number 5 into base 3.
Step 2: Find the largest power of 3 that is less than or equal to 5. The powers of 3 are 1 (3^0), 3 (3^1), and 9 (3^2). The largest power 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 3^1 place.
Step 4: Subtract 3 from 5. This gives us 2 (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).
Step 6: Determine how many times 1 (3^0) fits into 2. It fits 2 times. So, we write down 2 for the 3^0 place.
Step 7: Now we have our base 3 number. We have 1 in the 3^1 place and 2 in the 3^0 place, which gives us 12 in base 3.

Base Conversion – Understanding how to convert a decimal number to a different base, specifically base 3 in this case.
Place Value System – Recognizing the significance of each digit's position in a number based on the base being used.