In a base-5 numeral system, what is the representation of the decimal number 12?

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Question: In a base-5 numeral system, what is the representation of the decimal number 12?

Options:

Correct Answer: 23

Solution:

In base-5, the decimal number 12 is represented as 22 (2*5^1 + 2*5^0 = 12).

In a base-5 numeral system, what is the representation of the decimal number 12?

In a base-5 numeral system, what is the representation of the decimal number 12?

Step 1: Understand that base-5 means we use digits 0, 1, 2, 3, and 4.
Step 2: To convert the decimal number 12 to base-5, we need to find how many times 5 fits into 12.
Step 3: Divide 12 by 5. The result is 2 with a remainder of 2 (12 ÷ 5 = 2 remainder 2).
Step 4: The quotient (2) tells us how many '5s' are in 12, and the remainder (2) is what is left over.
Step 5: Write the base-5 number using the quotient and remainder. The base-5 representation is 22 (which means 2*5^1 + 2*5^0).

Base Conversion – Understanding how to convert a decimal number to a different base, specifically base-5 in this case.
Place Value System – Recognizing how each digit in a numeral system represents a power of the base.