40.2*10^-19/40.96

asked by guest
on Nov 28, 2024 at 1:56 am



You asked:

Evaluate the expression: \(\frac{40.2 \cdot {10}^{-19}}{40.96}\)

MathBot Answer:

\[\frac{40.2 \cdot {10}^{-19}}{40.96} = \frac{201}{2048000000000000000000} = 0.00000000000000000009814453125\]

\[\begin{aligned}\frac{40.2 \cdot {10}^{-19}}{40.96}& = \left(40 + \frac{2}{10}\right) \cdot \frac{1}{10^{19}} \cdot \frac{1}{40 + \frac{96}{100}}\\& = \left(40 + \frac{1}{5}\right) \cdot \frac{1}{10^{19}} \cdot \frac{1}{40 + \frac{96}{100}}\\& = \frac{201}{5} \cdot \frac{1}{10^{19}} \cdot \frac{1}{40 + \frac{96}{100}}\\& = \frac{201}{5} \cdot \frac{1}{10000000000000000000} \cdot \frac{1}{40 + \frac{96}{100}}\\& = \frac{201}{5} \cdot \frac{1}{10000000000000000000} \cdot \frac{1}{40 + \frac{24}{25}}\\& = \frac{201}{5} \cdot \frac{1}{10000000000000000000} \cdot \frac{1}{\frac{1024}{25}}\\& = \frac{201}{5} \cdot \frac{1}{409600000000000000000}\\& = \frac{201}{2048000000000000000000}\end{aligned}\]

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