(15.22*10^3)(140.48*10^-6)/(8.314)(295.75)

asked by guest
on Sep 19, 2024 at 7:32 pm



You asked:

Evaluate the expression: \(\frac{15.22 \cdot {10}^{3} \cdot 140.48 \cdot {10}^{-6}}{8.314 \cdot 295.75}\)

MathBot Answer:

\[\frac{15.22 \cdot {10}^{3} \cdot 140.48 \cdot {10}^{-6}}{8.314 \cdot 295.75} = \frac{2672632}{3073581875} \approx 0.00086954963579748465298325589586\]

\[\begin{aligned}\frac{15.22 \cdot {10}^{3} \cdot 140.48 \cdot {10}^{-6}}{8.314 \cdot 295.75}& = \left(15 + \frac{22}{100}\right) \cdot 10^{3} \cdot \left(140 + \frac{48}{100}\right) \cdot \frac{1}{10^{6}} \cdot \frac{1}{\left(8 + \frac{314}{1000}\right) \cdot \left(295 + \frac{75}{100}\right)}\\& = \left(15 + \frac{11}{50}\right) \cdot 10^{3} \cdot \left(140 + \frac{48}{100}\right) \cdot \frac{1}{10^{6}} \cdot \frac{1}{\left(8 + \frac{314}{1000}\right) \cdot \left(295 + \frac{75}{100}\right)}\\& = \frac{761}{50} \cdot 10^{3} \cdot \left(140 + \frac{48}{100}\right) \cdot \frac{1}{10^{6}} \cdot \frac{1}{\left(8 + \frac{314}{1000}\right) \cdot \left(295 + \frac{75}{100}\right)}\\& = \frac{761}{50} \cdot 1000 \cdot \left(140 + \frac{48}{100}\right) \cdot \frac{1}{10^{6}} \cdot \frac{1}{\left(8 + \frac{314}{1000}\right) \cdot \left(295 + \frac{75}{100}\right)}\\& = \frac{761}{50} \cdot 1000 \cdot \left(140 + \frac{12}{25}\right) \cdot \frac{1}{10^{6}} \cdot \frac{1}{\left(8 + \frac{314}{1000}\right) \cdot \left(295 + \frac{75}{100}\right)}\\& = \frac{761}{50} \cdot 1000 \cdot \frac{3512}{25} \cdot \frac{1}{10^{6}} \cdot \frac{1}{\left(8 + \frac{314}{1000}\right) \cdot \left(295 + \frac{75}{100}\right)}\\& = \frac{761}{50} \cdot 1000 \cdot \frac{3512}{25} \cdot \frac{1}{1000000} \cdot \frac{1}{\left(8 + \frac{314}{1000}\right) \cdot \left(295 + \frac{75}{100}\right)}\\& = \frac{761}{50} \cdot 1000 \cdot \frac{3512}{25} \cdot \frac{1}{1000000} \cdot \frac{1}{\left(8 + \frac{157}{500}\right) \cdot \left(295 + \frac{75}{100}\right)}\\& = \frac{761}{50} \cdot 1000 \cdot \frac{3512}{25} \cdot \frac{1}{1000000} \cdot \frac{1}{\frac{4157}{500} \cdot \left(295 + \frac{75}{100}\right)}\\& = \frac{761}{50} \cdot 1000 \cdot \frac{3512}{25} \cdot \frac{1}{1000000} \cdot \frac{1}{\frac{4157}{500} \cdot \left(295 + \frac{3}{4}\right)}\\& = \frac{761}{50} \cdot 1000 \cdot \frac{3512}{25} \cdot \frac{1}{1000000} \cdot \frac{1}{\frac{4157}{500} \cdot \frac{1183}{4}}\\& = \frac{761}{50} \cdot 1000 \cdot \frac{3512}{25} \cdot \frac{1}{1000000} \cdot \frac{1}{\frac{4917731}{2000}}\\& = \frac{761}{50} \cdot 1000 \cdot \frac{3512}{25} \cdot \frac{1}{2458865500}\\& = 15220 \cdot \frac{3512}{25} \cdot \frac{1}{2458865500}\\& = \frac{10690528}{5} \cdot \frac{1}{2458865500}\\& = \frac{2672632}{3073581875}\end{aligned}\]

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