(22.241 × 0.508³)/(3 × 69×10⁹ × 1.78×10⁻⁷)

asked by guest
on Nov 17, 2024 at 10:45 pm



You asked:

Evaluate the expression: \(\frac{22.241 \cdot {0.508}^{3}}{3 \cdot 69 \cdot {10}^{9} \cdot 1.78 \cdot {10}^{-7}}\)

MathBot Answer:

\[\frac{22.241 \cdot {0.508}^{3}}{3 \cdot 69 \cdot {10}^{9} \cdot 1.78 \cdot {10}^{-7}} = \frac{1980786361}{25031250000000} = 0.000079132538\overline{76654182272159800249687890137328339575530586}\]

\[\begin{aligned}\frac{22.241 \cdot {0.508}^{3}}{3 \cdot 69 \cdot {10}^{9} \cdot 1.78 \cdot {10}^{-7}}& = \left(22 + \frac{241}{1000}\right) \cdot \left(\frac{508}{1000}\right)^{3} \cdot \frac{1}{3 \cdot 69 \cdot 10^{9} \cdot \left(1 + \frac{78}{100}\right) \cdot \frac{1}{10^{7}}}\\& = \frac{22241}{1000} \cdot \left(\frac{508}{1000}\right)^{3} \cdot \frac{1}{3 \cdot 69 \cdot 10^{9} \cdot \left(1 + \frac{78}{100}\right) \cdot \frac{1}{10^{7}}}\\& = \frac{22241}{1000} \cdot \left(\frac{127}{250}\right)^{3} \cdot \frac{1}{3 \cdot 69 \cdot 10^{9} \cdot \left(1 + \frac{78}{100}\right) \cdot \frac{1}{10^{7}}}\\& = \frac{22241}{1000} \cdot \frac{2048383}{15625000} \cdot \frac{1}{3 \cdot 69 \cdot 10^{9} \cdot \left(1 + \frac{78}{100}\right) \cdot \frac{1}{10^{7}}}\\& = \frac{22241}{1000} \cdot \frac{2048383}{15625000} \cdot \frac{1}{3 \cdot 69 \cdot 1000000000 \cdot \left(1 + \frac{78}{100}\right) \cdot \frac{1}{10^{7}}}\\& = \frac{22241}{1000} \cdot \frac{2048383}{15625000} \cdot \frac{1}{3 \cdot 69 \cdot 1000000000 \cdot \left(1 + \frac{39}{50}\right) \cdot \frac{1}{10^{7}}}\\& = \frac{22241}{1000} \cdot \frac{2048383}{15625000} \cdot \frac{1}{3 \cdot 69 \cdot 1000000000 \cdot \frac{89}{50} \cdot \frac{1}{10^{7}}}\\& = \frac{22241}{1000} \cdot \frac{2048383}{15625000} \cdot \frac{1}{3 \cdot 69 \cdot 1000000000 \cdot \frac{89}{50} \cdot \frac{1}{10000000}}\\& = \frac{22241}{1000} \cdot \frac{2048383}{15625000} \cdot \frac{1}{207 \cdot 1000000000 \cdot \frac{89}{50} \cdot \frac{1}{10000000}}\\& = \frac{22241}{1000} \cdot \frac{2048383}{15625000} \cdot \frac{1}{207000000000 \cdot \frac{89}{50} \cdot \frac{1}{10000000}}\\& = \frac{22241}{1000} \cdot \frac{2048383}{15625000} \cdot \frac{1}{\frac{368460000000}{10000000}}\\& = \frac{22241}{1000} \cdot \frac{2048383}{15625000} \cdot \frac{1}{36846}\\& = \frac{22241}{1000} \cdot \frac{2048383}{575718750000}\\& = \frac{1980786361}{25031250000000}\end{aligned}\]

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