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jmc

prealgebra senior

Problem

Express

4. \overline{054}

as a common fraction in lowest terms.

Solution

Let

x = 4. \overline{054}

. We then have

1000 x = 4054. \overline{054}

, so

1000 x - x = 4054. \overline{054} - 4. \overline{054} = 4050 \Rightarrow x = \frac{4050}{999} = \frac{150}{37} .

Final answer

\frac{150}{37}