If a number in base-3 is represented as '210', what is its decimal equivalent?

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Question: If a number in base-3 is represented as \'210\', what is its decimal equivalent?

Options:

Correct Answer: 19

Solution:

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

If a number in base-3 is represented as '210', what is its decimal equivalent?

If a number in base-3 is represented as '210', what is its decimal equivalent?

Step 1: Identify the base of the number. Here, the base is 3.
Step 2: Write down the number '210' and identify each digit's position from right to left: 0 is in position 0, 1 is in position 1, and 2 is in position 2.
Step 3: Convert each digit to decimal by multiplying it by 3 raised to the power of its position:
Step 4: For the first digit (2), calculate 2 * 3^2. This equals 2 * 9 = 18.
Step 5: For the second digit (1), calculate 1 * 3^1. This equals 1 * 3 = 3.
Step 6: For the third digit (0), calculate 0 * 3^0. This equals 0 * 1 = 0.
Step 7: Add all the results together: 18 + 3 + 0 = 21.
Step 8: 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.