Question

Convert the base-ten number to a number in the indicated base
2874 to base five
Write the numeral base
200 six

Answer 1

Answer on Question # 41472, Math, Algebra

Convert the base-ten number to a number in the indicated base 2874 to base five, 200 to base six. Write the numeral base.

Solution.

$$\begin{array}{l} 2874 = 5^4 \cdot 4 + 374 = \\ = 5^4 \cdot 4 + 5^3 \cdot 2 + 124 = \\ = 5^4 \cdot 4 + 5^3 \cdot 2 + 5^2 \cdot 4 + 24 = \\ = 5^4 \cdot 4 + 5^3 \cdot 2 + 5^2 \cdot 4 + 5 \cdot 4 + 4 = \\ = 4 \cdot 5^4 + 2 \cdot 5^3 + 4 \cdot 5^2 + 4 \cdot 5^1 + 4 \cdot 5^0 \\ \end{array}$$ $$2874 = 42444_{five}$$ $$\begin{array}{l} 200 = 6^2 \cdot 5 + 20 = \\ = 6^2 \cdot 5 + 6 \cdot 3 + 2 = \\ 5 \cdot 6^2 + 3 \cdot 6^1 + 2 \cdot 6^0 \\ 200 = 532_{six} \\ \end{array}$$

Answer: $2874 = 42444_{five}, 200 = 532_{six}$

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