Math Problem Solver

\[ 0.2 + 0.22 + 0.222 = \frac{321}{500} = 0.642 \]

The sum can be computed by rewriting each term over a common denominator, where the least common denominator of \(\frac{2}{10}\), \(\frac{22}{100}\), and \(\frac{222}{1000}\) is \(1000\). \[ \begin{aligned} 0.2 + 0.22 + 0.222 &= \frac{2 \cdot 100}{10 \cdot 100} + \frac{22 \cdot 10}{100 \cdot 10} + \frac{222 \cdot 1}{1000 \cdot 1} \\ &= \frac{200 + 220 + 222}{1000} \\ &= \frac{642}{1000} \\&= \frac{321}{500} \end{aligned} \]