If the number 'A' in a base-6 system is equal to 30 in decimal, what is the valu

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Question: If the number \'A\' in a base-6 system is equal to 30 in decimal, what is the value of \'A\'?

Options:

Correct Answer: 42

Solution:

In base-6, \'A\' = 3*6^1 + 0*6^0 = 18 + 0 = 18. Therefore, \'A\' is 42 in decimal.

If the number 'A' in a base-6 system is equal to 30 in decimal, what is the value of 'A'?

If the number 'A' in a base-6 system is equal to 30 in decimal, what is the value of 'A'?

Step 1: Understand that 'A' is a number in base-6. This means it uses digits from 0 to 5.
Step 2: The number 'A' is given as '30' in base-6.
Step 3: Break down the base-6 number '30'. The first digit '3' is in the 6^1 place, and the second digit '0' is in the 6^0 place.
Step 4: Calculate the value of 'A' in decimal: Multiply the first digit by 6 raised to the power of its position: 3 * 6^1 = 3 * 6 = 18.
Step 5: Multiply the second digit by 6 raised to the power of its position: 0 * 6^0 = 0 * 1 = 0.
Step 6: Add the two results together: 18 + 0 = 18.
Step 7: Therefore, the value of 'A' in decimal is 18.

Base Conversion – Understanding how to convert numbers from one base to another, specifically from base-6 to decimal.
Place Value – Recognizing the significance of each digit's position in a number system, particularly in base-6.