In a base-5 numeral system, what is the representation of the decimal number 10?

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Question: In a base-5 numeral system, what is the representation of the decimal number 10?

Options:

Correct Answer: 20

Solution:

In base-5, the decimal number 10 is represented as 20.

In a base-5 numeral system, what is the representation of the decimal number 10?

In a base-5 numeral system, what is the representation of the decimal number 10?

Step 1: Understand that base-5 means we use digits 0, 1, 2, 3, and 4.
Step 2: Identify the place values in base-5. The rightmost digit is the 'ones' place (5^0), the next is the 'fives' place (5^1), and so on.
Step 3: Convert the decimal number 10 into base-5 by finding how many times 5 fits into 10.
Step 4: 5 fits into 10 exactly 2 times, which means we have 2 in the 'fives' place.
Step 5: After using 10 (2 times 5), there is no remainder, so we have 0 in the 'ones' place.
Step 6: Combine the digits from the 'fives' place and the 'ones' place to get the base-5 representation: 20.

Base Conversion – Understanding how to convert a decimal number to a different base, in this case, base-5.