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Fractional Equivalences

by Eugene Chen of the Amador Valley Math Team

The following table should be memorized in order to get an advantage on speed-based math rounds.

\begin{array}{|c|c|c|}\hline \textbf{FRACTION} & \textbf{DECIMAL} & \textbf{PERCENT} \\ [1ex]\hline\frac{1}{2}& 0...

Exercise 1: Memorize this table. Then, get a friend to quiz you on it.

Problem 1: Prove that \frac {1}{9} = 0.\overline{1} and \frac {1}{11} = 0.\overline{09}. Understanding how to do this will be very helpful in Lesson 3.

Hint: Let x = 0.\overline{1}. What can we do to this equation to eliminate the pesky repetition?