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# Number Theory

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For each part of this problem, convert the fraction to a "decimal" in the specified base.

(a) Convert the fraction $$\frac{1}{2}$$ to base $$3$$

(b) Convert the fraction $$\frac{1}{7}$$ to base $$8$$

(c) Convert the fraction $$\frac{1}{b - 1}$$ to base $$b$$

I already have the solutions to parts a and b, but I included them for context. It would be great if someone helped explain c. I know the answer to c, but not why and how it's proven. It'd be great if someone explained that. Thank you!

Feb 23, 2020
edited by Guest  Feb 23, 2020