In a base-3 system, what is the decimal equivalent of the number '210'?

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Question: In a base-3 system, what is the decimal equivalent of the number \'210\'?

Options:

Correct Answer: 6

Solution:

\'210\' in base-3 is 2*3^2 + 1*3^1 + 0*3^0 = 18 + 3 + 0 = 21 in decimal.

In a base-3 system, what is the decimal equivalent of the number '210'?

In a base-3 system, what is the decimal equivalent of the number '210'?

Step 1: Identify the base of the number. The number '210' is in base-3.
Step 2: Write down the place values for each digit in '210'. The rightmost digit is 3^0, the middle digit is 3^1, and the leftmost digit is 3^2.
Step 3: Multiply each digit by its corresponding place value. For '210', this means: 2 * 3^2, 1 * 3^1, and 0 * 3^0.
Step 4: Calculate each multiplication: 2 * 3^2 = 2 * 9 = 18, 1 * 3^1 = 1 * 3 = 3, and 0 * 3^0 = 0 * 1 = 0.
Step 5: Add the results of the multiplications together: 18 + 3 + 0 = 21.
Step 6: The decimal equivalent of '210' in base-3 is 21.

Base Conversion – Understanding how to convert numbers from one base to another, specifically from base-3 to decimal.
Exponentiation – Applying the concept of exponents in the context of base systems to calculate the value of each digit.