In base ten, 111_five would be written: A) 421. B) 155. C) 31. D) 21. E) 555.

Question

Quizplus · Accepted Answer

The given number is in base five. To convert it to base ten, we use the place values in base five, which are powers of 5. Starting from the right, the place values are $5^0, 5^1, 5^2, \ldots$. Thus, the number is $1*5^4 + 1*5^3 + 1*5^2 + 1*5^1 + 0*5^0 = 625 + 125 + 25 + 5 = 780$ in base ten, which is not listed in the options provided. It seems there was a mistake in my calculation or interpretation of the options. Let's correct that:The correct interpretation should be: The sequence "111_five" seems to be a miscommunication. Assuming the intention was to present a number in base 5, and interpreting "S", "U", "B", and "five" as potential typographical errors or non-relevant characters, the closest meaningful interpretation based on the provided options would be to consider a number in base 5, such as "11111" (if we only consider the digits and ignore letters).Converting "11111" from base 5 to base 10:$$1 \times 5^4 + 1 \times 5^3 + 1 \times 5^2 + 1 \times 5^1 + 1 \times 5^0 = 625 + 125 + 25 + 5 + 1 = 781$$However, this calculation does not match any of the provided options, indicating a misunderstanding in the question's interpretation. Given the options and assuming a simpler case based on the digits provided:If we were to simplify the question to converting a base-5 number to base-10 and assuming a typo in the question, the correct approach for a base-5 number "111" (as a simplified, reasonable guess based on the question's format) would be:$$1 \times 5^2 + 1 \times 5^1 + 1 \times 5^0 = 25 + 5 + 1 = 31$$This matches option C) 31, under the assumption that we're dealing with a simplified interpretation due to the confusion in the question's presentation.

In Base Ten, 111five Would Be Written

In Base Ten, 111_five Would Be Written