(1.68*10^-8)*10/16.6*10^-6

asked by guest
on Oct 24, 2024 at 11:26 pm



You asked:

Evaluate the expression: \(\frac{1.68 \cdot {10}^{-8} \cdot 10}{16.6} \cdot {10}^{-6}\)

MathBot Answer:

\[\frac{1.68 \cdot {10}^{-8} \cdot 10}{16.6} \cdot {10}^{-6} = \frac{21}{2075000000000000} = 0.00000000000001\overline{01204819277108433734939759036144578313253}\]

\[\begin{aligned}\frac{1.68 \cdot {10}^{-8} \cdot 10}{16.6} \cdot {10}^{-6}& = \left(1 + \frac{68}{100}\right) \cdot \frac{1}{10^{8}} \cdot 10 \cdot \frac{1}{16 + \frac{6}{10}} \cdot \frac{1}{10^{6}}\\& = \left(1 + \frac{17}{25}\right) \cdot \frac{1}{10^{8}} \cdot 10 \cdot \frac{1}{16 + \frac{6}{10}} \cdot \frac{1}{10^{6}}\\& = \frac{42}{25} \cdot \frac{1}{10^{8}} \cdot 10 \cdot \frac{1}{16 + \frac{6}{10}} \cdot \frac{1}{10^{6}}\\& = \frac{42}{25} \cdot \frac{10}{100000000} \cdot \frac{1}{16 + \frac{6}{10}} \cdot \frac{1}{10^{6}}\\& = \frac{42}{25} \cdot \frac{10}{100000000} \cdot \frac{1}{16 + \frac{3}{5}} \cdot \frac{1}{10^{6}}\\& = \frac{42}{25} \cdot \frac{10}{100000000} \cdot \frac{1}{\frac{83}{5}} \cdot \frac{1}{10^{6}}\\& = \frac{42}{25} \cdot \frac{10}{100000000} \cdot \frac{5}{83} \cdot \frac{1}{10^{6}}\\& = \frac{42}{25} \cdot \frac{10}{100000000} \cdot \frac{5}{83} \cdot \frac{1}{1000000}\\& = \frac{21}{1250000000} \cdot 10 \cdot \frac{5}{83} \cdot \frac{1}{1000000}\\& = \frac{21}{125000000} \cdot \frac{5}{83} \cdot \frac{1}{1000000}\\& = \frac{21}{2075000000} \cdot \frac{1}{1000000}\\& = \frac{21}{2075000000000000}\end{aligned}\]

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