1+ $0.2^{2}$- $0.2^{3}/6$-0.2

asked by guest
on Oct 24, 2024 at 4:21 am



You asked:

Evaluate the expression: \(1 + {0.2}^{2} - \frac{{0.2}^{3}}{6} - 0.2\)

MathBot Answer:

\[1 + {0.2}^{2} - \frac{{0.2}^{3}}{6} - 0.2 = \frac{629}{750} = 0.838\overline{6}\]

\[\begin{aligned}1 + {0.2}^{2} - \frac{{0.2}^{3}}{6} - 0.2& = 1 + \left(\frac{2}{10}\right)^{2} - \left(\frac{2}{10}\right)^{3} \cdot \frac{1}{6} - \frac{2}{10}\\& = 1 + \left(\frac{1}{5}\right)^{2} - \left(\frac{2}{10}\right)^{3} \cdot \frac{1}{6} - \frac{2}{10}\\& = 1 + \frac{1}{25} - \left(\frac{2}{10}\right)^{3} \cdot \frac{1}{6} - \frac{2}{10}\\& = 1 + \frac{1}{25} - \left(\frac{1}{5}\right)^{3} \cdot \frac{1}{6} - \frac{2}{10}\\& = 1 + \frac{1}{25} - \frac{1}{125} \cdot \frac{1}{6} - \frac{2}{10}\\& = 1 + \frac{1}{25} - \frac{1}{750} - \frac{2}{10}\\& = 1 + \frac{1}{25} - \frac{1}{750} - \frac{1}{5}\\& = \frac{26}{25} - \frac{1}{750} - \frac{1}{5}\\& = \frac{779}{750} - \frac{1}{5}\\& = \frac{629}{750}\end{aligned}\]

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