If 'XYZ' in a base-6 system equals 215 in decimal, what is the value of 'X'?

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Question: If \'XYZ\' in a base-6 system equals 215 in decimal, what is the value of \'X\'?

Options:

Correct Answer: 4

Solution:

215 in decimal is \'543\' in base-6, so \'X\' is 4.

If 'XYZ' in a base-6 system equals 215 in decimal, what is the value of 'X'?

If 'XYZ' in a base-6 system equals 215 in decimal, what is the value of 'X'?

Step 1: Understand that 'XYZ' is a number in base-6, which means each digit represents a power of 6.
Step 2: Convert the decimal number 215 into base-6. We will do this by dividing 215 by 6 and keeping track of the remainders.
Step 3: Divide 215 by 6. The quotient is 35 and the remainder is 5. This means the least significant digit (rightmost) in base-6 is 5.
Step 4: Now take the quotient 35 and divide it by 6. The new quotient is 5 and the remainder is 5. This means the next digit in base-6 is also 5.
Step 5: Take the new quotient 5 and divide it by 6. The quotient is 0 and the remainder is 5. This means the next digit in base-6 is 5.
Step 6: Now we have all the digits: from the last division to the first, we have 5, 5, and 5. So, 215 in decimal is '555' in base-6.
Step 7: Since 'XYZ' in base-6 equals '555', we can see that 'X' is the first digit, which is 5.

Base Conversion – Understanding how to convert numbers between different bases, specifically from decimal to base-6.
Place Value in Different Bases – Recognizing how the place values work in a base-6 system and how they differ from the decimal system.