(16.71*10^3)(140.48*10^-6)/(8.314)(295.15)

asked by guest
on Sep 19, 2024 at 2:43 pm



You asked:

Evaluate the expression: \(\frac{16.71 \cdot {10}^{3} \cdot 140.48 \cdot {10}^{-6}}{8.314 \cdot 295.15}\)

MathBot Answer:

\[\frac{16.71 \cdot {10}^{3} \cdot 140.48 \cdot {10}^{-6}}{8.314 \cdot 295.15} = \frac{2934276}{3067346375} \approx 0.00095661710197303687295504734121\]

\[\begin{aligned}\frac{16.71 \cdot {10}^{3} \cdot 140.48 \cdot {10}^{-6}}{8.314 \cdot 295.15}& = \left(16 + \frac{71}{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{15}{100}\right)}\\& = \frac{1671}{100} \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{15}{100}\right)}\\& = \frac{1671}{100} \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{15}{100}\right)}\\& = \frac{1671}{100} \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{15}{100}\right)}\\& = \frac{1671}{100} \cdot 1000 \cdot \frac{3512}{25} \cdot \frac{1}{10^{6}} \cdot \frac{1}{\left(8 + \frac{314}{1000}\right) \cdot \left(295 + \frac{15}{100}\right)}\\& = \frac{1671}{100} \cdot 1000 \cdot \frac{3512}{25} \cdot \frac{1}{1000000} \cdot \frac{1}{\left(8 + \frac{314}{1000}\right) \cdot \left(295 + \frac{15}{100}\right)}\\& = \frac{1671}{100} \cdot 1000 \cdot \frac{3512}{25} \cdot \frac{1}{1000000} \cdot \frac{1}{\left(8 + \frac{157}{500}\right) \cdot \left(295 + \frac{15}{100}\right)}\\& = \frac{1671}{100} \cdot 1000 \cdot \frac{3512}{25} \cdot \frac{1}{1000000} \cdot \frac{1}{\frac{4157}{500} \cdot \left(295 + \frac{15}{100}\right)}\\& = \frac{1671}{100} \cdot 1000 \cdot \frac{3512}{25} \cdot \frac{1}{1000000} \cdot \frac{1}{\frac{4157}{500} \cdot \left(295 + \frac{3}{20}\right)}\\& = \frac{1671}{100} \cdot 1000 \cdot \frac{3512}{25} \cdot \frac{1}{1000000} \cdot \frac{1}{\frac{4157}{500} \cdot \frac{5903}{20}}\\& = \frac{1671}{100} \cdot 1000 \cdot \frac{3512}{25} \cdot \frac{1}{1000000} \cdot \frac{1}{\frac{24538771}{10000}}\\& = \frac{1671}{100} \cdot 1000 \cdot \frac{3512}{25} \cdot \frac{1}{2453877100}\\& = 16710 \cdot \frac{3512}{25} \cdot \frac{1}{2453877100}\\& = \frac{11737104}{5} \cdot \frac{1}{2453877100}\\& = \frac{2934276}{3067346375}\end{aligned}\]

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