(20*0.05) /(5*21.8)
You asked:
Evaluate the expression: \(\frac{20 \cdot 0.05}{5 \cdot 21.8}\)
MathBot Answer:
\[\frac{20 \cdot 0.05}{5 \cdot 21.8} = \frac{1}{109} = 0.\overline{009174311926605504587155963302752293577981651376146788990825688073394495412844036697247706422018348623853211}\]
\[\begin{aligned}\frac{20 \cdot 0.05}{5 \cdot 21.8}& = 20 \cdot \frac{5}{100} \cdot \frac{1}{5 \cdot \left(21 + \frac{8}{10}\right)}\\& = 20 \cdot \frac{5}{100} \cdot \frac{1}{5 \cdot \left(21 + \frac{4}{5}\right)}\\& = 20 \cdot \frac{5}{100} \cdot \frac{1}{5 \cdot \frac{109}{5}}\\& = 20 \cdot \frac{5}{100} \cdot \frac{1}{109}\\& = 20 \cdot \frac{5}{10900}\\& = \frac{100}{10900}\\& = \frac{1}{109}\end{aligned}\]