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jmc

number theory intermediate

Problem

What is the base ten equivalent of

10101 0_{5}

?

Solution

10101 0_{5} = 0 \cdot 5^{0} + 1 \cdot 5^{1} + 0 \cdot 5^{2} + 1 \cdot 5^{3} + 0 \cdot 5^{4} + 1 \cdot 5^{5} = 5 + 125 + 3125 = 3255

Final answer

3255