In a base-5 numeral system, what is the representation of the decimal number 7?

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Question: In a base-5 numeral system, what is the representation of the decimal number 7?

Options:

Correct Answer: 12

Solution:

In base-5, the decimal number 7 is represented as 12, since 1*5^1 + 2*5^0 = 5 + 2 = 7.

In a base-5 numeral system, what is the representation of the decimal number 7?

In a base-5 numeral system, what is the representation of the decimal number 7?

Step 1: Understand that we need to convert the decimal number 7 into base-5.
Step 2: Identify the largest power of 5 that is less than or equal to 7. The powers of 5 are 1 (5^0 = 1), 5 (5^1 = 5), and 25 (5^2 = 25). The largest power we can use is 5 (5^1).
Step 3: Determine how many times 5 fits into 7. 5 fits into 7 one time (1 * 5 = 5).
Step 4: Subtract the value of 5 from 7. 7 - 5 = 2.
Step 5: Now, we need to represent the remaining value (2) in base-5. The largest power of 5 that fits into 2 is 1 (5^0 = 1).
Step 6: Determine how many times 1 fits into 2. 1 fits into 2 two times (2 * 1 = 2).
Step 7: Since we have used 1 time of 5 and 2 times of 1, we can write the base-5 representation as 12 (1 for 5^1 and 2 for 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.