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jmc

prealgebra senior

Problem

Express

1. \overline{27}

as a common fraction in lowest terms.

Solution

Let

x = 1. \overline{27}

. We then have

100 x = 127. \overline{27}

, so

100 x - x = 127. \overline{27} - 1. \overline{27} = 126 \Rightarrow x = \frac{126}{99} = \frac{14}{11} .

Final answer

\dfrac{14}{11}